It depends what you're after. (I have memberships on both)
Bear in mind that chess.com regularly has 10 times the number of players online at any one time, so it's much easier to find a game of your desired time controls and ability level.
Also, chess.com has much better material and functions to improve your rating for lower and intermediate rated players. For this reason alone I would recommend chess.com to lower ability players (although these features require a premium membership).
chessclub.com (ICC) has a greater number of GM's, etc. There are GM's and IM's on chess.com, but not as many as far as I can tell.
Finally, chess.com has outstanding "social" features, like teams and forums, etc, trolls notwithstanding.
So, I would without hesitation recommend chess.com for learners and intermediate players, and ICC for those who want to play against higher-rated players. I spend most of my time on chess.com and don't intend to extend my ICC membership.
UPDATE:
chessclub.com: 897 players currently online.
chess.com: 22,235 players currently online.
There was a time when chess.com didn't exist, and chessclub.com was the place to go. ICC's website now is a dog's breakfast and has been lacking in development for a long time. IMO, ICC had relied too much on the number of GM members at attract players. Chess.com, although more expensive, is a much more vibrant and educational place to be.
ICC pissed me off when I let my subscription lapse for 9 months and wouldn't reactivate my account that I had for 15 years. I had ~ 15000 blitz games under my handle and dozens of contacts. All gone and they couldn't care less.
