I own both .44's and .36's and I prefer the .36 in every respect.
My latest want is a Pietta 1862 Colt Police in .36 caliber. This is basically a 1860 Sheriff's Model (5-1/2" barrel) but in .36 caliber. It's not "period correct" but it is the best of the 1851 Navy with the looks of an 1860 army, plus a gorgeous six-shot, fluted cylinder.
As far as velocity goes, .36 is faster, but the heavier .44 has more energy.