LogFAQs > #880818067

Up to you if you want to look at these, but I'm gonna tell you what you get for doing the memories. My only spoiler-free version is: It's not worth focusing so much over. I'd say you probably shouldn't look at these tags, but if you're not enjoying the game that much anyway, maybe they're more good than harm:

The reward for doing all the Divine Beasts is removing half the HP from the final boss and, as you probably already know, the special abilities for each Champion.

The reward for doing all the memories is a minor change in the ending cutscene. I also think doing so might unlock one shrine quest, but I'm not 100% sure if that one is actually tied to doing the memories.