Well, some tube mics sound more demonstrably "tubey" than others. Kind of a thicker slower sound, although we are talking nuance here -- it's not like cranking your guitar amp up. Of the tube mics I have, the GT MD1a probably has more of that sound than the others. The other tube mics I have are a couple GT AM-40/GT-44 (same mic with different cosmetics), a GT MD3, and a Neumann Gefell M582h. The other mics sound comparatively "hi-fi" compared to the MD1a, although the Neumann is somewhat warmer than the other GT mics. IMHO the Neumann and the MD3 seem more suited for vocal work and the MD1a and the AM40/GT-44 seem more oriented towards instruments (although they do sound pretty decent on vocals as well).
I've only heard the term "break up" in reference to loud dirty guitar amps. Why would you want a mic to "break up"??? If you mean what I think you mean, then you would just be destroying the diaphragm.....