Meh, I disagree. I started playing Q3 Arena, and it's a whole lot of fun. Quake Live doesn't feel like Quake, not really. Maps don't have the same atmosphere, and some minor tweaks to the maps make it seem as if even a bad player can beat you, just from strategy alone. I guess that's a plus for a lot of people...
Also, all weapons are nerfed like no other. QL also puts a huge reliance on the rocket launcher.
But, the community for Q3 Arena seems to have degraded a lot. The only servers I've played so far are all instagib... ugh, so boring. Single player ROCKS on Nightmare, though. So difficult, took me 3 days of straight play to beat it. Xaero's a bitch on the last map

So, playing Q3 Arena improves your raw skill, in my humble opinion. At least, it does if you play through single player on Nightmare. Haha. My favorite game is to get as many gaunts as I can

Q3A and QL are very much different. Weapon damage is WORLDS different. Map layout is incredibly different, even though only the smallest of changes are made to the structure and the spawns. In my opinion, play both. You can find a good torrent for Q3A to play single player, and I bet it's probably only $10 to buy at this point.