We've worked with a couple of barrel MFG's and found the same trend with both 5R and 5-groove traditional rifling.
At the end of the day 4-groove seems to be a traditional carryover from forever ago. Most everything that was made around the time countries adopted smokeless powder was a 4-groove barrel. There are some exceptions in the mid/late 1800's black powder era stuff, but the Krag, Mausers, M1903, Swiss straight pulls (after the 1889 BP rifle), Mosin Nagants, etc.. Pretty much every popular rifle except the Lee Enfield (5G, LH) was 4 groove. There were some war-time simplifications in WWII to make 2-groove barrels but those are exceptions to the rule.
I don't know where 6-groove made it's introduction but now it's often used in SAAMI cartridge introductions-- and as far as I can tell that's purely because the groundwork has already been done and it's an easy cut/paste option.
All of that being said, it's usually not make or break any way. However, when given the choice (unless it costs dramatically more for some obscene reason) I opt for 5 groove-- Ideally 5R. 4G and 6G seem to have a higher propensity to cause bullet failures if you're pushing the limits but tight spots, burrs, and other manufacturing defects can cause the same thing regardless of rifling style. 4G with sharp corners also seems to do a bit better on the whole with short bearing surface match/varmint bullets (think short range BR)... But again for what we're doing I haven't ever seen any compelling evidence that it's meaningfully different between 4G, 5G, 5R, or 6G. Barrel-to-barrel variation still seems to trump rifling type/profile.
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