The Shawnees are solid. The Supremes as others have mentioned, are the Cadillac. But beyond seeming a more, shall we say 'finished' overall product, the Supremes appear to be offered in more varying dimensional layout as well as options / colors, etc. Someone mentioned the Shawnees only had one mold, which isn't right as they do provide a couple of different commissary widths as well.
All of that being said, I would think that a big decider for all but the most patient would be the fact that last I heard, the Shawnee's were a 2-3 YEAR wait. I know there was some talk about recent ownership change so I can't say if they've ramped up production but it used to be one at a time. My brother that bought 3-4 of them over the last 15 years waited 1-2 years for the last 2. Matter of fact, still waiting on last 1. But he does love 'em. When my River Rat goes, it'll be for the Supreme unless an absolutely irresistible deal happens along on a Shawnee. Right place, time & money does sometimes yields a fire sale..
PS. One other thing. Last I knew, the (possibly previous) owner of Shawnee was pairing them up with the easyloader trailers, which seem to be a heck of a nice rig.
I think I've got some good picture of a few Shawnees. I'll post 'em if I can dig them up.