Like several others, I have both Browning and Ruger single shots. Comments above are all valid on some level.
My own experience is that MY Rugers are more accurate than My Brownings. Others, obviously, have different experiences.
My most accurate rifle is a Ruger #1 in 30=-06 that will print 1/2" grouops all day with Remington 180gr. Bronze Tips.
As far as hunting goes, the Rugers win out.
Generally lighter weight and the need to cock the hammer on a Browning, that's half hidden under a scope, with gloves, on a cold morning is a clear negative.