Intel seems to have a significant advantage in terms of power/price range. It's too bad because AMD was rightly underrated in the past with their older series but seem to have lost their game.
Anyway, if you're looking to build a $300 system, is this from scratch, or do you have a monitor, keyboard, and mouse? Can you use an old case or any other parts? If no, $300 will be pretty tight, but I think doable. I'll go check, unless you're looking to get a preconfigured one from a supplier.