I rather play Quake 3 than live. Why not play Quake 3?
I play Q3A from time to time but QL has a much larger foothold in my region. I would also rate QL as the better game in general because of the 80 rail, much larger map pool, and better rulesets (like built-in CA and the better TDM rules).
Having said that, Q3A and QL are so similar that I'd play either depending on where the players are. Where I live, the players are on QL.
Two points:
1) The direct comparison between Quake Live and Quake Champions is not completely fair. Quake Live is a product of the process that started when Quake 3 was released in 1999, both the game and its players have evolved during the past 17 - 18 years. Quake Champions has not even been released yet, and I reckon that the game and the way how it is being played will change a lot during the next 10 years.
2) With every release of new sequel to a popular FPS franchise, there are always veteran players calling the new game compromised, or worse than the one of the previous games. I have been one of those people. My experience with the Tribes franchise shows that the new players do not see the new game as compromised product or weaker if they enjoy the game. After some time, these players will begin to see the new game as the best version. I am sure there were QuakeWorld and Quake 2 veterans who saw Quake 3 as a compromised product, but after 17 years of Quake 3 and Quake Live, no one cares or remembers.
The first point I'd agree with. I'm certainly not writing this game off; indeed, I anticipate putting in a lot of hours should they clean up the netcode. I'm not expecting a drastic difference in how the game is played coming about, however. The mechanics are still fundamentally similar to Q3A.
I don't agree at all with the second point, however, mostly because your line of reasoning doesn't apply to me at all. When I was really getting into Quake I came to the conclusion pretty quickly that Quake 2's multiplayer was a downgrade from the original's and I still believe it. I also think Quake 4 is quite a bit worse than every other Quake game and have for years; that's unlikely to change. Quake Champions, in its current state, isn't a game that I will one day come to believe is better than QL unless certain things change. As is, the only selling point over QL/Q3A is the presence of players (...and the fact that the client doesn't crash every time I try to join a new game).