I don't really shop at supermarkets in Budapest, but I have friends who do and who also regularly go to Austria. They swear the better-quality Hungarian produce is sold in the Austrian supermarkets and often for less than the lower-quality stuff costs in BP.
We know of a Hungarian sheepherder who sells his lamb meat rather to Austria and Italy than Hungary. The "for less" is not true, the very reason he sells it abroad is because no one in Hungary would pay the price he asks for quality meat.