Like all with magnum revolver rounds, a longer barrel gives more velocity, and my 18" Marlin carbine really gets a lot out of the .357 Mag cartridge. So I guess that in a purely single-minded sense, the long sight radius and velocity advantage 8 3/8 inches "is best for utilizing the best that the .357 mag cartridge has to offer" if no other criteria is considered.
However the handling and handiness factor steps in eventually when the thrill of initial ownership dims - and you may come to the same conclusions as revolver greats like Elmer Keith and Skeeter Skelton that the 4" to 5" revolver barrels are the best all-around lengths.
I have both 6" and 4" .357 Mags. The 6" was my first and I felt that I needed that extra length at the time. This length was also the common length owned among all of my friends. I have found that personally I have come to prefer the handiness of the 4" - so that would be my preference if I only could own one. Actual chronographing both of mine shows a loss in velocity for the 4" compared to 6 in most, but not all loads - but nothing really significant in the real world. So 4" to 6" works for me.
I have also shot the 8 3/8" version and found them fairly unwieldy for most uses and would not recommend this length. Ballistically-speaking, this barrel length performs better, but not enough that I would consider it worth the trade-off as to it's handling. If all you ever did with one was hunt deer and Silhouette competition, they would be great.
When it comes to the snubbie versions, they tend to be very "blasty" and the sight radius is short, so you start getting handicapped a bit here. The .357 Mag is a long-range handgun cartridge that can really reach out there with the right loads and shooter, so sight radius can be a limiting factor here. So I think that the 2 1/2" to 3" barrel versions are more of a specialized type.