Longer barrel lengths give a longer sighting radius and if the powder is slow burning enough you will develop more velocity.
Most loads in .357/.38 special will not be slow enough burning to take advantage of the added barrel length. Sighting radius most likely will be the main gain.
I wouldn't think for the range of shots you would be making that there would be much if any advantage of round barrel over octagon. Unless you are shooting some exotic loads (Leverloution Ballistic tipped bullets) or extra hot loads that you would be shooting much over 100 yards.
If you want an authentic look, I would go with the octagon barrel. I wouldn't think you would be mounting a scope on this rifle.