The Quarantine Balls are equivalent to standard Poke Balls in terms of capturing power, and are more for story purposes than anything. I don't know about the other three, we haven't been introduced to them properly. In any case, most balls (Basic Quarantine Ball being the exception) have bonuses attached to them that make catching Pokemon easier, and are the only way to apply negative bonuses to Pokemon you want to capture at all.

Oh, yes, if you want to buy any Poke Balls, do so in packs of ten. That's one free Premier ball, and unlike the games, they have a slight benefit attached to them (-2 off captures), so it's worth it.