Thinking of saving for a bari sax. Looking at the costs a Low Bb Mark Vi and a W01 Yani seem to be in about the same price range. Which if these is a better horn for playing . . . well, I'm interested in composing my own work is for my YouTube videos. Think "Sketches of Spain" or minimalist type music. Low A is not vital. Don't need a "classical" horn, yet it isn't jazz either.
If you are looking at a Mk VI, condition matters - do your homework BEFORE YOU BUY to find a tech to give you a quote on an overhaul. Offhand, I would budget $1500-$2000 on top of the cost of the horn, unless it has a recent overhaul by a good tech.
Beyond that, if you are focusing on the sound of the horn, play each and listen to the recorded product. If you hear a difference, then you will likely have a preference. If you don't hear a difference, then it doesn't matter. Either can play well enough to exceed your needs.
My favorite bari for a solo voice in a small ensemble was a Buescher TrueTone, next was a low Bb Mk VI. I much prefer the weight and balance of a low Bb bari, if you don't need a low A. Low A baris tend to have a lil' more grunt on tap, if that's a consideration - I believe that may be due to the taper of the bell, but I've not put the theory to any test, nor do I recall it being discussed at SotW.
Enjoy your quest.