The way Guy explained it to me was the fire ring method has a groove in both surfaces and there's a ring that sits in the groove. You then get a head gasket that goes outside the ring and the ring keeps the fire away from the gasket.
O-ring has a .035 groove in the block and uses a .040 wire like you see in the bag in the picture. That method uses a regular head gasket and just has extra pressure right where the fire ring sits. Both are supposed to hold up well with high hp and boost.
As far as disadvantages I wouldn't know any. I think anything you can do to keep from having to tear a fully built motor apart is a no-brainer