Enuma Gremory's life was without a shadow of a doubt a massive improvement over the life of Harriet Potter. She was actually loved and accepted for who she was and she loved her family in return. Rias Gremory was a great big sister and Sirzechs was a great big brother… even though he could be a bit annoying at times.
While Enuma didn't gain the Power of Destruction from the Blood Adoption, she did gain a massive increase to her magical reserves, not that she really needed the hereditary ability of the Bael-clan since the Gate of Babylon made her on par with her big sister. The versatility, power and sheer size of the armory that was the Gate of Babylon more than making up for Enuma's lack of the Power of Destruction. The fact that she didn't need the Power of Destruction made itself especially clear when she whipped out the possibly most destructive artifact in the Gate of Babylon, Ea, the Sword of Rupture, and unleashed the technique she chose to be her name when she officially changed it. Enuma Elish. The amount of destruction that Enuma Elish caused took months to repair.
The massive increase of Enuma's magical reserves wasn't the only change that the Blood Adoption caused. The most notable one was that Enuma's looks changed to something resembling a mix between her parents. Her formerly black hair was now crimson red and her formerly green eyes were now violet. Which made her look like a younger version of Rias with only difference besides age being the eye color.
One of the more notable events that happened during Enuma's childhood was the day a few days after her eighth birthday. The day she met and recruited the first member of her own Peerage. Her Queen. The last surviving member of a Vampire-clan. Shalltear Bloodfallen. Enuma found the vampire on the brink of death, begging for help and a chance to live, abandoning any semblance of pride that would have stopped her from accepting servitude. Not that she ever regretted her decision. Despite being centuries older than her King, Shalltear got along well with Enuma. Something that both surprised and fascinated Enuma was Shalltear's ability to shape-shift. While the Vampire claimed that she could change her appearance quite extensively, she mostly preferred to simply alter her appearance to change her physical age, usually going with the look of a buxom teenager. And despite what most would think, given how Shalltear liked to dress, she wasn't flat.