Welcome to FT, shannonk.
I think AA or CO will absolutely comp elite if you have ALREADY ATTAINED elite status on a competitor and have the card and recent mileage statements to prove it to them. I don't think they will comp elite if you're only halfway to elite status on DL.
As for which to go for, I've been CO elite for years and love it because of the couponless, unlimited domestic upgrades. But many have been frustrated with CO's refusal to confirm upgrade award travel internationally. If you're going to Europe a lot I'd concentrate on AAdvantage; if not, CO. Good luck.
[This message has been edited by BearX220 (edited 05-03-2001).]