I didn't participate in the other thread because it was rehashing all the old notions - from both sides. Here's my take on the hardware issue.
I'm kind of a minor hardware junkie. I like to toy around with how hardware changes affect my playing, and I've learned something:
Of course all of this assumes the hardware is in good repair, professionally designed, properly adjusted, and played with a proper embouchure, air support, intonation, etc.
Beyond that, hardware mostly affects feel, which I define as experience behind the bell. For roughly equivalent horns, the experience 15 feet in front of the bell is mostly the same. The interior bore profile effects resonance, resistance, and articulation. 95% of what players talk about with relation to specific horns is behind the bell stuff. Some of this affects how the player plays (small bores articulate differently than large bores).
For example:
http://butlertrombones.com/?page_id=100
Scroll down to the Brass Vs Carbon video. On Facebook, the listeners who voiced an opinion got it right about 50/50. So if you can't even tell the difference between materials as wildly different as brass and carbon fiber, can anything else (except geometry) make any difference in the sound of a horn at all?
Valve trombone and baritone sound different due to geometry, but yellow and red brass bells are really only different behind the bell - to the player. The sound difference in front does exist, but against other factors, it is comparatively so small that you can't hear it.
Each player has their own "accent" on the horn, mostly created by your slide technique, articulation inflections, and various playing habits. But if Joe Alessi and George Roberts each played a Bb scale on a 547 horn with precisely controlled articulations, you'd be hard pressed to tell them apart.
Does hardware make a difference? Yes, the feel matters to the player. Geometry (mouthpiece inside shape, leadpipe inside shape, bore profile and bell taper) are what matters to the listener, but only so much. I don't think you could tell the difference between my 88h w/547 slide vs 525 slide if I were playing with an orchestra. You might be able to hear it if I play a solo. While the difference in feel behind the bell may be significant, the sound differences in front of the bell are subtle.