Now that the groove vs velocity question has been answered, let's circle back to the original question, what is/are the reason(s) that one would choose a 4, 5R or 6 groove barrel rather than one of the others?
The one thing I do believe in with the 5R (and this doesn't apply to all odd groove barrels) is that the odd number of lands and grooves the lands don't directly oppose one another. This will distort/upset the bullet jacket less and this will help fight bullet failure. Bullet failure is higher in the smaller calibers like .224 and 6mm. Not much of a problem in 6.5's and bigger calibers.
Bullet failure is more of a problem for a long range shooter then a short range shooter. I've seen it personally with 6mm bullets and I did trace it back to the lot of bullets had a problem with them. Most shooters take the bullets for granted and as soon as they have a problem with accuracy or anything else they are quick to point the finger at something else and usually don't think of the bullet.
An even groove/land barrel the lands will directly oppose one another. Also in 3 groove barrels because the lands are much wider you still get part of one land opposing another so you don't get the true benefit of the 5 groove/5R type barrel.
For the most part the number of grooves has no bearing on accuracy either. The only exception to this rule is with 6mm with short jacket bullets like the 65-68gr. bullets with the 6ppc type guns. Those short jacket bullets don't like the 5R rifling. I tell guys they will shoot in the upper .2xx's to flat .3xx's but that's all you will get out of them. So I'm against making a 5R barrel for a PPC shooter because of this. My 6PPC has a conventional 5 groove barrel and it's a hammer. it's not a 5R.
Shooting bullets over say 85gr. in 6mm the longer bearing surface of the bullet has more for the rifling to bite on to and they don't seem to care.
I've shot barrels from everything from 2 groove up to 8 groove in calibers from .22rf up to .338cal. and for the most part I don't see a difference with the style or number of grooves with the exception of the short jacket 6mm's I described earlier.
I do lean towards the 5R cleaning easier from a carbon fouling stand point vs. conventional rifling. This is because the patch isnt' trying to get down into a 90 degree corner next to the land. As far as copper fouling goes I don't see a difference. Some say the copper fouling cleans easier in a 5R style barrel but I don't see a difference.
Some say if you want hard core accuracy you want conventional style rifling (not 5R, polygonal, ratchet etc...) but the question I put back to guys are these...What are you using the gun for? What are your accuracy requirements? Then I go from there.
Later, Frank