I have both, and you really can't go too far wrong with either. Overall though, I'd recommend the Paasche H. I find the Paasche to be a little simpler and the Paasche's paint adjustment under the tip to be easier to adjust compared to the Badger's which is at the end of the body. Theoretically, the Badger's design should provide a bit better paint quality, but in practice, I find that I cannot see any difference between the two; they are both excellent. Contrary to popular mythology, the fact that they single action airbrushes does not prevent you from getting fairly fine lines or painting free-hand soft edge camo.
Rather than buying the HS1, I would suggest going for the H Set, which at $50 dollars is still a bargain. It comes with a 6' braided hose, color cup, small and large bottles, as well as #1, #3, and #5 tips.