I don't feel real warm and fuzzy about universal background checks, but even that is preferable to registration. Registration is the first step on the road to confiscation.
The problem is that the current bill, as written, is so badly written that any gun owner of any gun will be a felon unless they never let another living soul touch their rifle without a background check and keep it stored in a locked container only they have access to.
One example: If my buddy comes to my house and I show him my new gun - legal. If I drive to my buddy's house to show him the same new gun - felon, no more guns.