There are significant differences between them, and I've enjoyed both. I mostly played full ring until recently, but in the last month or so have found the 6-max games profitable enough to switch.
You can make a profit at full ring games with a relatively straightforward strategy, especially at games like Omaha High/Low. You can play tight, because the blinds aren't coming round too fast, so you're always playing premium hands, not the tricky ones.
In 6-max, if you try to just play the standard ultra-tight game recommended in most poker books
, you'll be more visible as not having played a hand, and will get no action when you do play, while the blinds coming round more will eat you up, so you'll lose more waiting for a hand and then get paid off less. Instead, you need to see a few more flops, defend your blinds more often (though not invariably), and pay more attention to the other players to work out where you are in those tricky hands. You'll have more of a chance to steal or bluff, although as always this is an over-used strategy by many, and the less you use it the more likely it is to work when you do.
In all, you have to bring more elements to your game to play 6-max well, and the swings can also be enlarged - getting dealt bad hand after bad hand the blinds are hitting more, and you're seeing more missed flops. Where I've found it most beneficial is in having more opportunity to isolate someone on tilt, so you're playing heads up (or at most 3-handed) with them, and can take more of the chips from their bad play.
It's better to start on full ring, though, to get a solid strategy fully functional, IMO, and you can then build on that to do well at 6-max