In my brief stint with a crosshair reticle on a BR scope I found myself aiming more and trying to acquire the center whereas my eye catches the dot quicker and I can confirm my POA faster.
I did feel as though I could aim more precisely, however, so who knows....personal preference, six of one, potatoe/potaaahtoe.
What I have done is order a scope with a dot, and if I find myself yearning for a crosshair I will sell/trade mine for what I am looking for.
Best of luck,
Mike