Yeah this is a fight. (Incidentally, I like Brainy more than Batman as a character anyway. he's a loveable dick, Batman can just be.....irritating.)
But yeah, Brainy wins. If this was one of the younger Brainy's, I'd say Batman has a shot. (3boot Brainy he would flat out own cuz that kids just too full of himself.) Adult Brainy, while still a dick, is a lot smarter and less inclined to make childish mistakes that the Primitive might be able to take advantage of.