Happ Comps are the stick I always use for fighting games. The Ultimates don't do diagonals very well. Happ Supers are decent, but I prefer those more for anything but fighters. As far as Neo games go, you'd be good with a Super or Comp, if you play more fighters I'd get a Comp. If you grew up playing fighters and coinop games in the USA, most likely you were using Happ controls.
I don't mind the japanese style sticks, but I don't want one for my full time stick and I find them too small/low to the base of the stick. They are made for small Japanese hands, and I definitely don't have small japanese hands (but a lot of fanboys like Kernow do).
However, be advised that Happ never made the comps, they are really the iL 8-Way Eurojoystick and Happ would buy those in kit form and re-brand them.
However Happ doesn't use the Eurojoystick anymore, and now makes the comps themselves in China. But the iL 8-Way Eurojoystick is still the same old comp we all know, so if you want a comp, don't buy from Happ, get the iL 8-Way Eurojoystick from lizardlick.com.