Kilsho, you are right, the tube stage is a little warmer in tone, but lacking slightly in detail. I find the player on the warm side of neutral anyway and the SS output is sufficiently without digital grain and glare, to make Classical enjoyable. You do seem to need to hear the detail in classical, which is often musically more complex than rock.
I have noticed other users saying they prefer the SS output, but having tubes gives you 2 different sounds to switch between