I'm no expert on Hill grips but I have owned a couple (straight and dished). I found little difference in shootability between the grip styles. Its mostly a minor comfort preference/aesthetic issue...and thats up to the individual.
Regardless of the grip style, much more important to how they shoot is how you place your hand on the grip itself. The 'suitcase hold' seems the best...solid and consistent, not to mention it reduces the perceived handshock in the bow hand. Handshock can either be just a thump with the proper grip or a 'teeth rattler" with the wrong grip. Once you get the right feel (with some practice) they really are neat, fun bows.
I stupidly sold both my Hills several years ago but recently purchased another from a fellow TradGang member (it'll be coming next week...thanks, Jim!). After playing with recurves and hybrids for some years I thought I'd ended my Hill-style mood. Nope! A Liberty Contender longbow just changed my mind (mild R/D, D-profile bow not far from a Hill style...another TradGang purchase...thanks, Rick!). They are great fun to shoot once you dial your style with them and work out that grip thing. And as far as accuracy at normal ranges, these bows give up nothing to other bows. My groups with the Liberty, at regular hunting ranges with fairly heavy wood arrows, are as good as with my recurves and aluminum arrows. I expect the soon-to-arrive Hill to be similar. The recurves with aluminums are still (for me) a better choice for the 3-D range where shots are longer, but there's room for both on my bowrack for sure.
Interesting bows, those Hills. Have fun with yours!