Fascinating question. With regard to performances (of classical), at least by the masters, it will be -- in my view -- a combination of both. Each performance will be slightly different, of course, but with the real masters the overall shape and so on will be very much the same every time through; they will have thought through their interpretation and polished them. Which is not to say there won't be subtle differences from performance to performance; there will be -- and it is these subtle differences which can make a tremendous difference in the end result, where the audience will sometimes come away with the feeling that wow this was really good playing to a feeling that they have been part of something really special and transcendent -- and never be able to figure out why.
In the case of jazz, though, within rather broad outlines spontaneity is far more important.
Now recordings are a different story altogether. There are really two kinds of classical recordings, and it can be very hard to know which you are getting. Almost all recordings today are engineered rather heavily, and put together from several (sometimes many!) takes. In my humble opinion, while this results in recordings where genuine mistakes or bobbles just don't exist, the end result will lack that subtle spontaneity -- and be very good and worthwhile, but lack that little something. There are, occasionally, recordings which are the result of a single take (they may be from a choice of several single takes, but the recording is all from one take; no editing). These can be and often are really stunning.