I would say that 30" dominates the gun rack except at skeet shoots.
When I first started trap and pigeons it was 30" and 28" respectively, then more trap shooters went up in length (barrels only) and for pigeons it started splitting 28 and 30 and 32 about equally. Sporting seems more 30/32, Bunker 30/32 and even skeet shooters are drifting from 28" to 30".
I've serously tested a lot of barrels including a 33-inch one. No particular length in the 30- to 34-inch range has stood out. It seems impossible to me that in the vast range of barrel stiffnesses just in my gun safe, from light 303 tubes to my new 18.4 mm TM-9X which is the toughest barrel I've ever encountered (I may have killed that tree!) , that some overriding single number would cover the "harmonics" of all of them. What about those Berettas with the big stiffening rib below the singles. Doesn't that change things?
It was the second-tier Ljutic X73 which had the 33-inch barrel and the top-of-the-line Monogun which had the 34's and Al always said they shot the same, as mine seemed to, and I had several.
I think the answer to the question posed by this thread is "Some of each, depending way more on the individual barrel than its length."
PS Gary, I look forward to your testing. I hope you will use 40 yards, not the 38 you have used in the past. It just makes it easier to compare your results with the rest of the world. It's awful here too, so I can understand why you are holding off.
Barfin, maybe you weren't around for the Jack Seehase era. He was a Florida guy who had worked for NASA - designed the Redstone rocket single-handed, in fact - and had a HP 46 calculator and that was enough to convince me!
It was his assertion that barrel vibrations accounted for _everything_ about patterns, including their very existence. Without vibrations, shotguns and rifles would shoot the same.
You handed him your gun and some money and he took it to a secret facility in his garage and worked over its vibrations with an oscillator and, as far as I was concerned, Cobralube ®.
The best part was that is work was undetectable. No change, no damage, none of the residual radiation which often spoils my own efforts at choke work.
I informally tested two TM-1's some vets had down in Arizona and the way they performed was completely consistent with them being untouched TM-1's.