I think Consider Phlebas was more of a generic action/adventure yarn, whereas Player of Games is a good tour of The Culture (by contrasting it with Azad).
I read Consider Phlebas first and enjoyed the hell out of it, but definitely think that Player of Games is, in 90% of situations, is the "correct" introduction novel.
I couldn't get into Consider Phlebas---I found the 'protagonist' too deeply flawed and unlikable. Is it likely I'll enjoy his other work in light of this?
If your only issue was the unlikeable "antihero" protagonist, then maybe? Most of his characters tend to be, at best, morally ambiguous. I know I said so in the previous comment, but Player of Games isn't too bad - the protagonist isn't really a good guy, but he's also not an amoral killer-for-hire.
Excession might be a better bet, although a lot of the novel basically consists of reading emails between characters.
I read Consider Phlebas first and enjoyed the hell out of it, but definitely think that Player of Games is, in 90% of situations, is the "correct" introduction novel.