Some DC games, IMO, needed analog to control the game. At least I needed to use the analog stick to play at my best. Also IIRC, Sonic used the analog to move and the d-pad to look around, and definately could move at different speeds and turn slower or faster depending on how far the analog was pressed.
OTOH, most arcade type games (example: SoulCalibur) were designed for digital stick inputs, even though both the d-pad & analog stick worked. And I know a few people who do better with d-pad than analog stick control even in games designed for analog.
Which is one of the great things of the u360: you can try the game with it in analog mode, then try it in digital and see which one you play best. And all emus should be able to map a digital stick to the analog input, so even game like sonic are controlable with digital joysticks.
Still might want to try the games with your current setup, though. Remember, just because your stick is physically digital doesn't mean it can't be used (mapped) to the analog stick.