I have both........
I have a Catquiver II for rainy days and if I just feel like shooting without one, and also a Thunderhorn Boa strap on style.
I typically don't use a bow mounted quiver on Compounds but with my longbow and recurves I think it might be best to keep a couple extra arrows right in front of me.

If you get a bow mounted one definitely practice with it on......it really changes the behavior of any given bow with respect to feel and possibly tune.