cheap saxophone mouthpieces

Does it matter what brass instument mouthpiece you use?

I’ve played baritone for 6 years and have never used a new mouthpiece. My brother bought a new saxophone and decided to by a new mouthpiece (not reed) so it would sound better. So I was wondering if certain mouthpieces produce certain sounds or if the expensive ones play just the same as the cheap ones. (preferably on a baritone or trombone.)

Yes, it does matter. While any good musician can get a good sound out of a junkie mouthpiece-it is much easier to do with a good quality mouthpiece. Each mouthpiece size can have a different rim circumference, diameter, and thickness, as well as a different cup depth and shape.
All these dimensions go to create a better sound emanating from your instrument. For a baritone, I would suggest a bach 6.5al or a bach 5g.