I’ve been wondering... I have an F. Schmidt non Thayer valve bass trombone and an Edwards Thayer valve bass trombone. I love the smoothness of the Edwards design and how easy it is to play real low pedals, but I find that I can put more air through my F. Schmidt and have an easier time playing. What do you guys prefer?

On different horns, it's apples to oranges. Much more than the valves are different between those two horns.

No Thayer valve.

Thayer Valve

It's personal. The smaller the horn, the less I would be inclined to use an axial valve. I personally have a good relationship with resistance, which means I always prefer the feel of other valves, although I've played some axials, and I understand why they can be seductive to some people. I prefer rotaries, but hagmanns are nice, and there are a lot of variations of rotary valves. I have some old stock conn valves, which work great, and a horn with the oversize Kanstul CR, which once I got used to them they were also great.

You can probably make anything work, and people grow to like stuff for various reasons, not all of which are really valid from a musical point of view. Plenty of nostalgia, inertia, and folklore at work here.

My best shot at a real reason for liking rotaries is that the well-cared for older valves require almost no maintenance, and are super reliable. Newer valves require more maintenance during break-in, and some valve types require a lot of futzing around with. I'm glad trombones don't come with piston valves.

You have to develop your own preferences. It's like picking a favorite color based on someone else's experience.