Below is xcaliber's response to my inquiry.
"It generally depends on what type of bullet and what type of shooting you're doing. The differences are very slight, however, the 6 groove tends to handle the very heavy bullets a bit more consistently, while the 5R and 3R/3Groove afford a better gas seal behind the bullet, are easier to clean and allow for ever so slightly higher and more consistent muzzle velocities and reduced spin-drift at distance, at the expense of faster heat-generation. In ARs, I tend to prefer 6 Groove because it is a bit more robust and can handle the relative higher volume of shooting. If I was using a 5rd magazines and shooting very, very slowly, I might lean towards 5R or 3R."
