I'm sure it's been touched on but the frequent skill checks went a long way with keeping me engaged with the story and characters.
I ran my first playthrough as a female scientist with a propensity to persuade and lie her way out of conflict and an aptitude for medicine. Really focused on Science, Persuade, Lie, and Medical. Throughout the entire game, I was able to utilize those skills to reach the conclusion of most quests. Given the character was created to be more lover as opposed to fighter, it went a long way to actually feeling like an actual ROLE PLAYING game, and is something that's been somewhat neglected since (uncoincidentally) New Vegas.
Probably the most fulfilling example of this was the final mission. Not only could I relate to a certain character while talking the big bad down, but there came a time that I could have allowed an artificial intelligence to complete a daunting task that pretty much was life of death, but since my Intelligence & Science was high enough, I was able to do it myself, with some genuinely funny dialouge from my companions.
Vicar: "Well, it's been a good life."
Being able to successfully do it was dope and made it feel like you'd actually worked toward something over the last 20+ hours. It was basically the Stonecutter Quote.