Go get this book: http://www.moonrakerqh.com/tack/gfx/...bit-better.jpg
A fantastic book.
The main difference is the full cheek snaffle is more severe.
The loose ring snaffle has the same amount of pressure to the mouth as what you put into your hands, it has a bit more play in the horse's mouth.
The Full cheek snaffle sends more signal to the horse when you put pressure on the reins. The bar part of the snaffle is attached to the keepers on the bridal which puts some poll pressure. So when you pull on the reins, it will pull the bar forward a little bit, putting some pressure on the poll.
I would always try to ride your horse on a regular snaffle before working your way to a full cheek or anything else. You would be surprised how severe even the more "simple" bits actually are.