Gosh... Y'know, for me... Ruby, Sapphire, and Emerald actually have a lot of cool features I'd love to have back. I always think of the third generation as the generation of side quests. They packed that gen with stuff to do. And D/P doesn't really... have that. Once you defeat the Elite Four for D/P it turns... bleh. R/S/E had many features to keep you hooked on the line longer. (For me anyway)
I miss the secret bases, I really enjoyed decorating those. XD Yeah sure, we have those underground bases in D/P, but do I really want to go underground every time I want to go to my secret base? No! In R/S/E I used to have base next to Lilycove city. I had my base at Route 120, near the lake. I always enjoyed visiting that route. One of the best routes ever in a game by my standards.
Another thing, mixing records with friends. I loved that fan club that always rooted for your friends sometimes and kinda like fueled you to do well. XD Good times. And finally, as others have said. Re-battling the gyms. Oy, the PokéNav was a fun addition back then.
So yeah, those are just a couple of the features I really miss. =/