This shouldn't be an either/or thing. Any public facing profile, especially on a platform like LinkedIn which is large and has many eyes on it, is better than none if you're looking to get the word out. I've had a LinkedIn profile from nearly the beginning, and although I nearly never use it, I am occasionally contacted by people about work. If I spent even an iota of time filling out my profile and posting regularly, it would probably bring me many offers. (Whether they'd be what I'm looking for is another story.)

If I had to choose between a public facing profile or a broad in person network, I'd choose the in person network. But you really shouldn't discount the online profile, since it's free advertising for you.