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I thought of a few more things, OP.
1. The versus mode should have a bunch of in-game battles you can choose from, and have it compare with their Pokemon instead. (I.e. gym leaders, elite four, organized by game)
2. You should have a slide-out thing on tablets like in Google's music app (pic related) with all the things you would normally swipe to view.
3. It'd be nice if you could choose which pokedex you wanted to use.
These are all pretty big requests, sorry.