I heard Clark Terry perform with a big band in 1969, but it wasn't really his band. I have heard several other lesser performers in this kind of situation, all of them pretty entertaining, but no one as good as Clark Terry. (He also autographed my calculus book.)
I was raised on classical music and jazz, strictly LP stuff. For jazz, I mostly listened to combos (Brubeck, Mulligan, early Miles Davis, Chet Baker, Art Farmer, etc.), since these were more readily available on record albums. But I really preferred the big bands, especially Count Basie--and after Basie, Duke Ellington.
I also liked Woody Herman's revived orchestra in the '60s, and then Maynard Ferguson. Jimmy Smith, the jazz organist, also put out some really good big band records.
I never got into Buddy Rich for some reason.
I will say that their repetoir can vary widely from show to show and some concerts will undoubtedly be much better, Houston happens to be blessed with real good performances from these guys. When asked what they play, it can be anything from ragtime to Ellington to some of Sun Ra's 1950s cosmic compositions (like Interplanetary Galaxy and Rocket #9 Takes Off For The Planet Venus) and just a whole slew of jazz styles. The 2 CD singles collection gives an overview of every style Sun Ra's band ever touched on (some of the pieces are more experimental which I don't care for as much but then there are some great vocal group recordings that I had never heard).