Each horn has it's own set of characteristics and I play the one that I deem most appropriate for the job.
For example, my Yamaha rotary C (YTR-945) is a great all-around horn. It doesn't have that stereotypical "Rotary" sound, however. If I NEED that stereotypical sound, then, I've got my Kurt Laberer rotary C (or one of my rotary Bbs).
If I'm playing with a certain group, I often play my venerable Bach 239L 25H piston C because they have a preconception of what a "rotary" sounds like and that somehow it won't blend with the rest of the section. Alas, the director doesn't seem to get that I sound pretty much like me, regardless of the horn I play, the differences being in my accuracy and intonation when I'm not playing my preferred horns (meaning I'm not quite up to my usual standard when I have to play the Bach).
South Bay Brass
Silicon Valley Brass Band - A Traditional British Brass Band