I think it somewhat depends on the person / horse. I dont do showmanship, not a big showmanship or obsticle person but i've watched some friends show showmanship (and ammy) and i'd say its about a 50/50 mix between the two type of halters.
Either is acceptable, especially at a local show, but you will find that more go with a QH style halter. If you are showing at a Regional/Championship or National/World show, you will definitely want a QH style.
Ozark Mountain has some that look very nice (not bulky straps). I have one that cost 2x as much as in a fancier betathane one, but I actually prefer my less expensive ones from Ozark
I think if your wearing western clothing, hat, western boots, etc. then you should use a western style halter, one with some nice tooling and silver. Star Lake Tack has them (we got one there). Then if your more of an English style person probably the Arabian type halter would work. When we first started showing we saw more of the English dress but now it seems most everyone has switched to Western. I think either is fine as long as you don't "mix and match".