Great questions. I have always used the adhesive frames just because it seems to me that they would hold the reeds in place more reliably than frames without adhesive. Then again, since I haven't used the non-adhesive frames, that opinion is just speculation, so it would be nice to hear from a few different folks with more experience with the frame types on this.
For myself, I have used the MCA (medium crowned adhesive), SCA (small crowned adhesive), and the youth frames (adhesive) in my call making. Over time, I have graduated towards using pretty much only the SCA frames, as well. The MCA frames are just big enough to be a bit uncomfortable in my mouth, and the youth frames seem too small for my liking. In a pinch, I can use any of them, but I prefer the fit of the SCA frames. (referring to Pioneer frames above)