In Brawl there's really only one way to play Diddy viably, which is camp until you land a hit with a banana. You could be a bit more aggressive if you're a master of the character like Zinoto or ADHD, but the idea is the same.
In PM, Diddy's moveset becomes very similar to CF's in Melee, but with bananas and peanuts. Bananas aren't quite as good as they were in Brawl, but it's still a great strategy to camp with bananas and capitalize on tech chases. Disqo does this to great effect. Or, you can be aggressive and combo-oriented like CF and use your bananas as approaching tools with glide tossing/aerial glide tossing, like myself or AbstractLogic. Diddy's moveset, movement speed, long dash dance, and good recovery make him a very versatile character with a lot of very different playstyle options. Check out the video thread to see a lot of different possible strategies.