When Saruhiko thinks about Misaki, he often finds himself contemplating the unwavering loyalty that a dog might possess. A puppy, even. A stray canine that never forgets the kindness shown to it, and always remembers to be thankful for the food it finds in passing. Saruhiko thinks of a pack of wolves, the type of tightly knit family group he used to compare HOMRA to, and knows that he is exactly right. HOMRA is a pack, a gang, a 'family', but their leader is a liar and a fake. He picks up stray dogs, tames them, domesticates them, parts them from their wildness, and pays attention to them only when he has nothing better to do. He lures them in with aloof kindness and then keeps them at a distance so they don't see through to his flimsiness and ineptitude as a leader.
Saruhiko could see through Mikoto from the beginning and despised what he saw. He only ever stuck around in HOMRA because Misaki was there, awed and adoring of his supposed rescuer. Saruhiko still resents it when Misaki calls Mikoto their saviour because he's not, and because he feels like Mikoto never even intended on saving them in the first place. They followed him back, promised to be of use, and then they stayed. It was nothing as extravagant as Misaki never failed to imply.
He thinks that Misaki is a lot like one of those stray dogs, rescued and tamed, and now he's found a pack and Mikoto is his alpha. The only one Misaki ever talks about, the only one he feels any loyalty to, and the only one standing between Saruhiko and his best friend. There's something very sick about deliberately driving a wedge between two people who were once as close as two humans could possibly be. Saruhiko's not sure if Mikoto did it on purpose, a mode of spite that he slipped past Misaki's nose, but he would begrudge the Red King his relationship with Misaki all the same.
So he chose to leave HOMRA because he couldn't bring himself to respect his so-called 'king' and because Misaki no longer needed him. With the support of a family like HOMRA, there was no need for Saruhiko to remain. He wanted to stay, of course he did, but Misaki only paid him attention when Mikoto wasn't around. Selfish or not, Saruhiko hated that and refused to take it. So he reclaimed his spot as the center focus of Misaki's thoughts by leaving. By joining Scepter4, a group he chose to spite both Misaki's ignorance and Mikoto's nonchalance toward his own 'pack members'.
Munakata is not someone that Saruhiko feels an immense loyalty to, but at least he is a man that is worthy of his respect. He treats everyone equally and keeps his subordinates at a respectable distance. His relationship with Awashima is always questionable, but he figures that as long as it doesn't interfere with their work there's no reason to consider it an issue. He likes Saruhiko, calls him 'Fushimi-kun' with a teasing edge to his voice, but he doesn't smother him like HOMRA did and so he never feels excluded. He treats Saruhiko like an adult with a voice and makes use of his well-adjusted reasoning skills. Saruhiko has no proof, but he thinks Munakata knows why he left HOMRA, and he thinks he also knows why he chose Scepter4. He never says anything, though, and it makes him all the more respectable in Saruhiko's mind.
There are a plethora of different reasons that Saruhiko likes Scepter4 better than HOMRA, but mostly he just likes that no one is important to him there. That sounds dismal, but it makes sense in Saruhiko's mind. There are no Misaki's, no Mikoto's, nor Anna's or Totsuka's. There are subordinates that Saruhiko keeps in line and works with, but no one that would care excessively if he got himself killed on a mission. They would stand silently, bury his body, and then forget he ever existed in the first place. Some might find that depressing, but to Saruhiko it feels freeing. He doesn't have to worry about who he's leaving behind in Scepter4 because the only person who ever mattered to him is in HOMRA.
See, that's where the key difference between he and Misaki lies.
Misaki is loyal to the bone and lives to please his alpha, his 'Mikoto-san', and his supposed saviour.
Saruhiko feels loyal to neither the Red King nor the Blue King, no matter what beliefs Misaki tries to force upon him. No matter how many times Misaki tries to sell him his spiel on the importance on loyalty, or how he ought to learn some honour, some thankfulness, for fuck's sake. Saruhiko can only laugh and laugh because Misaki always misses out on the most defining feature of his character.
Saruhiko might just be the most loyal person out of their entire lineup of hooligans and soldiers alike, but very few care to look deep enough to realize it. Why look past the crazy, they say, and then move on like he doesn't matter. He sort of expected more from Misaki but he likes to think that his blatant ignorance can be blamed, again, on Mikoto taking up all his head space.
And it all comes right back to the fact that Saruhiko already knows loyalty, has tasted its burn and understands its immense pressure, because he has been loyal to someone all his life already. Misaki has never once seen it, but Saruhiko has always – always – been loyal to him. To Yata Misaki. Red, Blue, Silver, Gold – none of it meant anything when compared with Misaki. No matter which faction Saruhiko cared to belong to, if he had to choose between a team and Misaki, he would pick Misaki each and every single time.
He likes to hope that one day Misaki will see his loyalty and will reward him with some form of understanding, or acknowledgement at the very least, but he's not sure that day will come. Misaki is completely blinded to Saruhiko by his loyalty to Mikoto. It hurts sometimes, drives him insane on bad days, but as long as he knows Misaki is alive that's all he needs.
Maybe one day when he's worked up the confidence he'll tell Misaki how it really is, but today is not that day.