Yep, it all depends on the player and the team, I really dont think you could say one position is more important than another (aside from goaltending).
Ok, but if you have two equally talented players like Crosby, Malkin, or Ovechkin (opinion) then the position they play has to take effect. I'd take goaltending out of this equation too, because minus Brodeur or Luongo, there aren't too many out there that can steal Stanley Cups (I'm aware Luongo hasn't and Khabibulin was God when TB won the cup).
I see what you're saying when you say, "depends on the player and the team." If I'm the SJ Sharks and I already have an elite play-making center in Joe Thornton, then naturally Ovechkin would be the "better" player. Or if I'm the Atlanta Thrashers and I already have an elite goal-scorer (and nothing else...jk), my choice would easily by Crosby.
A center has to be good at all aspects of hockey - skating, stick-handling, shooting, offensive/defensive positioning, agility, stability, face-offs; he has to cover the center of his own net, dig in the corners in both zones, and essentially make things happen. A wing doesn't have to worry about face-offs, does not have to cover the front of his own net, does not get down low in the corners in the defensive zone, and can often get lazy without definite consequences. IMO a center of equal talent and determination will always be more valuable than a wing.
To simplify this, many see this debate as a goal-scorer vs a passer, and goal-scoring always seems to trump passing. Strange though that historically, the best teams are built around good passers. Gretzky's Oilers, Lemieux's Penguins, Messier's teams, Yzerman's Red Wings, the Sakic/Forsberg Avalanche. Pure goal scorers (Hull, Mogilny, Bure, Selanne, Kovalchuk, Cheechoo, Ovechkin?) have never had a championship team built around them. Brett Hull (perhaps the greatest goal-scorer of all time) got his two Stanley Cups when he became an added piece (to the Stars, to the Wings). Crosby makes the teammates around him always better because he essentially forces them to be apart the scoring, whereas Ovechkin creates his own chances a majority of the time.
When the playoffs come around, good coaches set defensive lines and shadows against pure goal scorers. This nullifies their skill and they can't win a cup. But good passers can find multiple different teammates to finish. This makes them much more valuable than a pure goal scorer. Ovechkin's highlight reel goals and body checks aren't going to amount to much against a well-coached playoff team.