i don't like BTN press because mechanically it puts the shoulder in a bad position and my shoulders are bad enough already to the point of preventing me from lifting at 100%. there is really not much difference, greater medial delt activation with BTN but, not a big deal as you can superset with side laterals before the overhead press in order to fully exhaust the medial delt.
though, i think for a natural, hypertrophy specific trainign should be discarded. i don't think you can make a lot of gains in size as a natural and you should instead focus on going heavy as hell, you know? do a power lifting routine, bands chains, explosive lifting, etc...