Back in 1994, I started out with Remington 3 in #5s because everyone told me they were a good compromise between #4s and #6s. I missed the first turkey I ever shot at... a bit on the far side it turned out, at about 40 yards.
I was determined not to let that happen again and began a full on quest to learn as much about shotgun ballistics (at least as they applied to turkey hunting) as possible. I read everything I could get my hands on, primarily articles by Jay Langston, former shooting editior of NWTF Turkey Call and contributor to T &TH. Jay constantly emphasized the importance of downrange energy for killing turkeys, even at the partial expense of pattern density. I switched to Federal 3 in #4s which made sense, given the open pastureland that I hunt in Missouri.
Do #6s pattern better out of my Winchester 1300? Slightly. But what may be misinterpreted as a "better" pattern may just be that there are 30% more pellets involved. The #4s still pattern well and I saw marked improvement in that about 5 years ago when Federal introduced their Flite-Control wad. Too tight a pattern is not always better for turkeys as anyone who has missed a 10-yard shot can attest.
It turns out that Jay's research on down range energy foreshadowed the Hevi-Shot revolution. More importantly, I have not missed a turkey in the ensuing 15 years and have made two kills at over 50 yards.
Hunting habitat and conditions should be a consideration when selecting shot size. I know Cut' n' Run hunts thick vegetation where shots are seldom longer than 20 yards or unobstructed, so in his case #6s probably make more sense. For the pastures of Missouri and farmland of Michigan that I hunt, #4s are the ticket.
"The joy of living is his, who has the heart to demand it." Teddy Roosevelt