Season 2
In this version Slade and Shado are lovers instead of her and Oliver, eventually Oliver is forced to make a choice between saving Shado and Sara and several of the prisoners on the AMAZO. Choosing to save the lives of the many instead of the one he cared about, Slade blames Oliver. (I always found Slade's reason for vengeance to be weak and so did Manu Bennet)
Oliver and Sara do not enter a relationship, them hooking up again was a mistake considering what them being together did to their families in the first place. As Oliver believes that vigilantes can't have relationships and he is slowly falling for Felicity at that point in time.
Additionally. Laurel and Sara's reconciliation is different as I disliked how Laurel was the one apologizing given everything Sara put her and their family through. Instead, Laurel explains to Sara all the events that happened to her since her apparent death. She tells Sara that for years she dealt with any grief or mishap like it didn't affect her but eventually couldn't do that anymore once Tommy died, so she instead started blaming others like the Arrow, Oliver, and eventually Sara. Laurel then mentions that she realizes that she has been unknowing blaming Sara for years, but Laurel tells Sara she is not at fault for her recent decisions as of late. She also tells Sara that as much as she has hated her and blamed her, she has loved and missed her more.
Additionally, I have also always felt that Laurel was never an alcoholic but suffering from major depression and goes to therapy for treatment.
Season 3 (In retrospect, 3 wasn't as bad 4 or 6 it just could have been better)
Sara's murder in the premiere, later causes Laurel to scream triggering her Canary Cry powers; revealing that Laurel was in Central City that night the particle accelerator exploded visiting her mother.
Additionally, Laurel having been kidnapped several times causes her to train even further in Boxing and Mix Martial Arts with Ted Grant during the several months between season 2 and 3, even taking a lover in the gym on the side for a little sub romance part.
Because of her powers, Oliver is less of dick and a hypocrite to her and is the one to encourage her to be the Black Canary instead of Felicity. Telling her that she is more of a hero than he or Sara ever will be and that she has a light in her that they don't possess which is why she was chosen to have these powers.
Showing more training sequences for Laurel, Roy, and Thea.
Less focus on Olicity.
More focus on Ra's al Ghul as an antagonist
Season 4
Oliver's son William is conceived in 2005 before he and Laurel became a couple, as it will give Oliver and Laurel less drama and it will fit the actor and character's age better.
Oliver's duel against Malcolm for the League should have been longer and more difficult given Malcolm's skill.
Quentin is the main character that is killed by Darhk, as he dies during the prison riot begging Darhk to kill him instead of Laurel as he can't bear losing a daughter again. During his final scene, he acknowledges Laurel for all that she has done for him admitting that even though he loves her and Sara equally; Laurel is the one he most proud of for always being there for him like she is always there for the people she loves. Likewise, he has final words with Oliver, acknowledging him as the closest thing he has to a son.
I really dislike Oliver learning magic to defeat Darhk, instead he and the team review everything they have learned about Darhk. Eventually they question why Darhk never faced Ra's al Ghul directly despite his power. They conclude, that the Lazarus Pit has something in it that makes others who have used the Pit for years or have been resurrected by the pit immune to Darhk's magic as it causes a mystical backfire when he uses his powers on them. This is particularly advantageous for Oliver and Laurel has they take the blood from their sisters (Thea's before she was cured by the Lotus) to combat Darhk by injecting in themselves.
During Thea's rescue operation, Laurel confronts Malcolm and after hitting him with her Canary Cry severely beats him. She tells him how much she hates him for getting the people she loves killed but most of all she is sick and tired of him justifying his selfish actions for protecting Thea. She makes it perfectly clear that if they survive Genesis, if she ever catches him in Star City or even catches a whiff of actions endangering her friends, she will hunt him down and shatter his skull from the inside with her powers. (Seriously, Oliver should have had this conversation long ago.)
In the final battle, all of Team Arrow battles Darhk and are partially immune to his powers thanks to Sara and Thea's Blood. Over the course of the battle the team slowly weakens Darhk, during the battle Darhk uses a spell to suppress Laurel's Canary Cry which leaves her unable to use it any further. Eventually, Laurel manages to kill Darhk in self-defense with one of Oliver's arrows.
In the end all the members of the team leave, except Oliver whose back to protect the city by himself. Felicity leaves to look after her mother whose heart broken after Quentin's death. Laurel leaves to travel the world because even after Darhk's death, she still can't use her powers, so she leaves to retrain herself to become a fighter as good as Oliver, Sara, Nyssa, and John.
Season 5
6 months later, Oliver continues protecting the city on his own, until Laurel comes back to visit now a highly skilled fighter with her skills impressing Oliver. She eventually returns to the team as a full time Black Canary, thinking the city needs her more as a vigilante than as a lawyer. She is also given a new Black Canary costume and a tonfa that can become a bo-staff.
Quentin's final words are revealed to Oliver, telling him to move forward in his life (the main theme of Season 5) so that he can become the man he always wanted to be and that when he becomes that man he will find his way back to Laurel, as Quentin believes for the first time that the two of them are meant to be.
John's stent in prison is much longer as instead breaking him out of prison, Oliver meets with him to tell John to not waste his life in prison. However, Barry does temporary break John out of prison for the Invasion crossover.
For a Legends Episode: Laurel wanting to spend time with Sara, meets up with the Legends to deal with an aberration in 9th century Norway. There they meet the Viking Prince Jon, and he and Laurel become lovers (Happened in the comics). During the episode Laurel and Sara come into verbal and even briefly physical conflict over their father's death but quickly patch things up.
Gradually over the course of the first arc, Oliver and Laurel's feelings for each other resurface especially after Laurel becomes troubled by Vigilante's actions after he brings up the needless deaths of many citizens including Quentin Lance who he mentions. Laurel and Oliver eventually kiss but later Laurel dismisses it as they were comforting in each other acknowledging that they don't work like that.
After the Invasion Crossover, Oliver now realizing that he's still in love with Laurel after being put in the Dominator's virtual reality tries to tell her. Eventually, after Oliver is tricked to kill Detective Malone by Prometheus; Oliver goes to see Laurel where he confesses to Laurel that he loves her, that they were getting married in the Dominator's reality, and that her very memory kept him alive during his five years in hell. Although hesitant, Laurel reveals to Oliver that she kept the photo she gave to him before he got on the Gambit, she also acknowledges that maybe the reason they haven't been able to move forward in their lives is because they have been doing it alone and maybe the people they are now can make their relationship work. This leads the two to passionately make love, while they are both unknowingly being watched by Prometheus.
Laurel finds herself unable to help John get out prison as his lawyer, due to Prometheus manipulation of the state department causing them to temporary suspend Laurel's legal license pending investigation. This causes Oliver to go ask Adrian for help with getting John out of prison, especially when John is placed in solitary confinement.
Instead of Black Siren, Prometheus releases Rainbow Raider (the guy who made Oliver and Barry fight in Flash vs Arrow), Raider causes rage induced riots and eventually affects Laurel; which cause her and Oliver to physically fight with Laurel bringing up all the pain he has caused her and her family. Eventually after defeating Rainbow Raider, Oliver and Laurel talk were Laurel assures him that while she has forgiven him for the pain he has caused her it does not mean she will ever forget it or be anger about it sometimes but that's for her to deal with and that she wouldn't still love him if she couldn't forgive him.
Laurel's time away from Star City is revealed, as she was secretly being trained by Talia al Ghul but only knows her as Miranda Tate (Dark Knight Rises ref). Talia has still been training Laurel since she returned to Star City by sending highly skilled fighters to fight her to increase her experience. Eventually Laurel comes face-to-face against Onyx Adams, a former CIA agent and combat specialist, looking for revenge against the Yazuka in Star City after one of them missed up her mission and ended her career. Laurel and Onyx fight, but Onyx defeats her, then Laurel faces her again and after a long and bloody battle Laurel comes out on top. Eventually Laurel begins showing signs of her powers returning and uses her Canary Cry to take down the Yazuka allowing her and Team Arrow to escape.
After calling John Constantine, Laurel learns that because Darhk was so powerful when he used his spell on her the effect took longer for her powers to return even with his death. Talia congratulates Laurel and offers her to travel with her to continue her training and to secretly save her from Prometheus's wrath. However, Laurel declines citing she needs to move forward and is rebuilding her life after her father's death.
After Oliver is tortured by Adrian, John and Laurel help Oliver breakthrough his trauma stating that his best friend and the woman he loves know him better than any psychopath ever could. Oliver also breaks down crying in front of Laurel, worried that know he'll always wonder if what he learned about himself is true.(I always thought that Oliver should have broken down in front of someone to show how really messed up chase affected him)
After Felicity breaks Cayden James out of prison. Oliver decides to leave Felicity be, but Laurel has problem with that considering she practically betrayed the team. Wondering if Oliver is still in love with Felicity, Laurel sadly leaves him afterwards he and Felicity are trapped in the Arrowcave. Eventually, Oliver apologizes to Laurel where tells he's sorry for how he was treating Felicity citing that does not want to lose her in his life, but he is not in love her anymore stating that in spite of all her great qualities Felicity does not have it in her to forgive someone when they make a mistake (which I've noticed in the Olicity Relationship and 1 of the reasons I dislike it). Oliver also reassures Laurel that she is the love of his life as in the Dominator reality he could have been with anyone, but his heart chose her like it always would.
Laurel fights Adrian evenly, but then Oliver faces him in the staircase. During Oliver's birthday, Oliver ask Laurel to move in with him which she agrees despite being a little reluctant.
As Felicity, John, and Laurel leave the city they are ambushed by Talia who reveals her true identity to Laurel. During the final show down on Lian Yu, Laurel and Nyssa face off against Talia together. Talia proves able to fight and gain advantage against both her student and half-sister, until Laurel knocks her out with her Canary Cry.