What will happen? Most often you'll be out a little more money, and with pretty much no difference in the performance of your ammo.
I've tried both, and I've seen no real reason to go for the BR primers. Many of my loads were accurate, regardless of which grade primer was used. I read they are mfg'd with better QC, more experienced employees, etc. But in all reality, the primers are what start the whole chain reaction of a round being spent, so they have to be made very carefully to begin with.
This is just my opinion, but taking into account that inconsistant/sloppy primers can cause pressure problems or spikes, they all (BR and standard primers) must be made very carefully (or in essence to the same standards), in order to remain completely safe for the reloaders, any companies that might use the primers for factory ammo, and for the safety of the primer manufacturers as well. Just my two cents.
-Patriot