I like both (although I never played Platinum).
I would like secret bases to make a return like they were in Hoenn but I would prefer them to be made with an item so they don't waste a move slot and I'd like them to have more relevance to the game apart from just being fun, like maybe NPC's discover it or maybe something that can be done over wi-fi. Maybe incorporate hidden grottos?
The house is awesome post game and a good way of incorporating rematches, no complaints if it returns. Except I heard that you still don't go there after beating the E4/Champ. That should be changed.