Monsters University and Inside Out are really tied up for my favorite slot, but I guess if I have to choose between them I'd go with the former.
Inside Out's got a deep (puns) plot that takes on a really strong meaning further in the film that I was personally able to identify with-- enough so that tears were shed for a while during the ending. But what Inside Out glaringly lacks is character development, being that the emotions are just that. They aren't really living their own lives so much as they are Riley's, and interrelationships between the emotions weren't shown off until really late in the film.
While Monsters University is a spin on a movie we already know and love. It takes us back to develop these wonderful characters further in an environment we can all relate to: school. It added a whole new cast of characters alongside the ones we're familiar with, and we got the chance to know and love them uniquely too. Whereas Inside Out was taking place in a panicked, stressful situation the entire time without much rest. Which leads to my next point about MU being lighter and more comedic in an also stressful situation, but having serious moments where it counts.
I've seen both movies more than once, but with MU I can't even count the number of times now hah.