I can think of no amps that will allow you to interchange those tube types. They have entirely different qualities, and amps that utilize each type will have their own strengths and weaknesses subject to your own personal preferences. I have 300B SET amps in my work system, and now am using my KT88 based amps at home (contrary to what you will see in my Virtual System). For Jazz and vocals I can think of no better way to listen, to my ears, than SET. Classical is a pretty broad category. If your classical tastes lean towards more dynamic and layered orchestral music, as Ctran60 points out, KT88 based amps may offer you a fuller, more forceful presentation. 300B SET is all about air, atmosphere, refinement, soundstage, holography. Sacrafice is often in the low end, and KT88 amps will almost certainly maintain an edge there. The best way to find out which you prefer is to try to listen to good examples of both. They are so different that the experience should leave you with an unmistakable impression of each I would guess. I enjoy each one for their strengths. For most acoustic music, vocals, jazz, small ensembles, I'll take SET every time. For orchestral music, or if you like any rock or perhaps bigger jazz bands, the KT88's would bring out the most there IMHO.
Hope that helps. Most important - Yes, they are very different and distinctive - listen and use your own judgement and take what you read here with a grain of salt. I think it is a good place to get some guideance and broad generalizations, but you're the only one who knows what you really prefer.
Marco