In my experience, if the balance is wrong for your individual style, you are (No Swearing Please) either way.
For me, shape, balance is the most important factor, they make the bat useable, the better (better as distinct from more) pressed it is, determines both the time (if any) it takes to play it in, and the longevity of its peak.
I guess to answer the very interesting question, it is important.... But no more important than other variables, so too does it depend on the specific circumstances of the user.