There are lots of generalists, but very few specialists in any particular area. On the other hand, most problems don't need a specialist in most areas.

Which approach is best depends largely on how much freedom you have to pick your area of work. If you're creating your own startup, being a specialist is great because you can make sure the problem you're working on is in your area of specialization -- myself, I'm working on online encrypted backups, and the areas of expertise needed (cryptography, security, data compression, concurrency) are precisely the areas which I'm most expert at. On the other hand, if you're joining your best friend from university to work on the startup idea which he picked, odds are that it's going to play to his areas of expertise, not yours, and you'd be better of being a generalist who can fill in the gaps after someone else does the heavy lifting of solving the "hard" problems.