I would opt for a sequel with improved features (set in the same village), rather than a remake. While I would like to see the game improved via addition of extra Pokemon, I'm not sure if that would be enough to justify a remake at this stage, but I think there is a lot more that could be done with some of the mechanics and concepts introduced in that game (and Super Mystery Dungeon isn't necessarily building on those).
That being said, if I were to re-release GtI, I would have more available Pokemon, more starters, etc. I miss the quizzes, but at this point, I don't really want the computer to pick my character for me (I did that for the first couple of games, but now I just have to game the quizzes to get the specific team I'm aiming for). Also, I would expand Paradise a bit, so there is room to make all of the different kinds of stalls simultaneously.