Gen III did introduce a lot of good things. However it had the crappiest story and the worst feeling of adventure.
Along with other problems I don't care to list (Spinda) it came before the Physical Special Split and even as a kid from before the split I hated that Fire Punch was a special move.
I actually felt like it had the best feeling of adventure because a lot of the areas were hidden and secretive (I played Ruby) or just unneeded. Specifically, the regis. THAT'S the type of ordeal crap I want to go through if I want to get legendary pokemon. That would probably be my favorite part about RSE. They made all the side legendaries difficult to get. Latios/Latias was a wondering pokemon, stereotypically hard. Rayquaza required the mac bike and had to do the bike thing to get to him. The regis, required an extensive knowledge of brail o.O. It also requires doing weird things like having a relicanth and wailord in a certain part of your party. and talking about weird pokemon team layout, ninjask was also cool when you evolve to it while you have an open slot on your team, you get a shedninja. That's what I feel like is missing in the newer pokemon games, everything feels like it's given to you. I don't count repelling my way through an obscure cave to find a legendary pokemon count as an ordeal to find a legendary pokemon. In fact, you had to do that if you wanted bagon (he's only found on this little island). Even feebas was cool to get (only popped up in 4 random tiles per game). I found this idea much better than the honey thing in DPP (it's more interactive and I don't have to wait real time for it).
So while the story or music is questionable, I definitely found RSE as having the best adventure because you actually have to find these pokemon instead of having it given to you (B2W2) in more ways than just going to the end of a cave (every other game).
The thing I didn't like about R/S/E was Mirage Island which was where they kept the Wynaut (or was it Wobbuffet?) You had to go and see this guy in Pacifidlog Town (I think) and hope that he saw it before you could go there; how to get the guy to do that was never explained or even hinted at. It must've been pure luck because whenever I visited him he never saw it. That and the current that would carry you past where you wanted to go (near Sootopolis City I believe) if you didn't navigate it right which I found exasperating.