The 2 differences of being a closer, just to re-state the obvious:
1. Bigger payday
2. Routine...knowing when you're going to pitch.
Of course, #2 is kind of a thing. In the book, Closer, Eckersley says:
"As soon as the phone rings when you are a relief pitcher, the most important part is knowing that the call is for you...You don't want to be surprised. And you can never be surprised when you are the closer. Again, it's all about the adrenaline. You can never get too used to it, but if you can channel it, you can be better than you can be. I'll tell you what; it makes you better than you are. Without the adrenaline I don't know how you can pitch..."
This feeds right into Cora's prepping approach. If Eckersley's opinion is correct for the typical reliever, knowing ahead of time when you'll probably be called upon is a thing, but even closers need to watch the game and manage expectations as the score and situation changes (e.g., team ahead by a run in the 8th...then behind by 4 runs). It's just easier if you know you're never pitching in certain situations, or certain to pitch in others.
Like many here, I trust Cora to do what he can. Still, I'm more concerned with the psychological impact of losing games in the 9th instead of the 7th. Both are losses, but the 9th inning one tears you apart. There's no getting around that.