Possibly blinded by nostalgia but GSC would have to be mine. I also love HGSS, especially with the addition of following Pokémon, but they do feel more "cartoony" in comparison. HGSS also dropped the room-decoration feature. Minor, but I enjoyed it. Also, connecting w/ Stadium 2 was far more entertaining than connecting to Battle Revolution. (HGSS did have mini-games of their own, but the PokéAthlon ain't my jam.)
In terms of story, my vote would probably go to BW.