The most hours logged would have to be either Diamond or X (both are around 450 hours, I believe). However, with Diamond, I had a tendency to put my DS down while it was still on and fall asleep, so my total playtime probably wasn't quite that high. I've gotten really into breeding on X (haven't done much lately, though), and that has added a lot to my timer.
It's strange, because I feel like I spent more time on Gold (257 hours when it died, I believe) and Red (hard to track because I restarted my save multiple times, but I think it was still significantly less than X and Diamond). I guess the in-person social element made those games seem like a bigger deal. I also feel like I've spent a ton of time training on LG (around 350 hours, I think; I've done very little breeding there, so that's probably the game with the most battling/training time).