VS MODEGoogle Friend Connect is really just a handful of widgets that let viewers have a "presence" on your site. Basically, within these widgets, Google / Yahoo users can talk to each other, discuss articles on the site, share pictures, etc, etc.
This is the solution you want if you're looking to add a "no touch" social networking angle to your site: you just drop in the widget code where you want it to appear, and off you go. The sites using Google Friend Connect right now are pretty lackluster looking; the best integration you'll find is Billboard for The People. This is programming-free social networking at its laziest.
Facebook Connect on the other hand, is for people who really want to dig in deep and have a much more fluid integration story. TechCrunch (see this story) is doing it right -- you can connect your Facebook account to TechCrunch, and never have to enter your name / email / website ever again. You even get the option of publishing your comment to your profile, if you feel it's good enough. There's probably oodles more they could do, but I'm not much of a man for oodles, so I'll pretend I never said that.
Since TechCrunch can perform deep integration using Facebook Connect, when you leave a comment as a Facebook user, the end result is fluid: the only difference anonymous comments and authenticated comments is the Facebook profile picture that shows up. It's got a funny blue 'F' in the lower right corner. Can't miss it.
Use Google Friend Connect if you've got a blog or regular static website and just want to slap on some pretty regular social networking features.
Use Facebook Connect if you need or want much better integration with your current site flow.