I did a few "one on one" tests, and from what I got, this is how it goes:
Each cubimal has a certain "ego" (= life points), according to their level. Higher level, higher ego.
Each attack takes away some ego. Still not sure if higher level attacks are stronger.
If a cubimal *chokes*, it has to skip it's next attack.
If you win, you get XP according to the level of your adversary. Defeating Level-1-cubis gets you 10 xp, defeating level-3-cubis gets you 30 xp, and so on.
The higher level you are, the more XP you need to level up. Same as for the Glitchen themselves. Two Level-6-cubis battling each other took them at least a couple of fights to reach leve 7.
The XP system seems to have been bugged at first, which would explain level 50+ cubimals roaming around Ur. Apparently that bug has been fixed.
We tried a whole lot of different combinations of "panache" vs. "gumption" and "wile" vs. "panache", and are still completely clueless if any of that has any impact whatsoever. If anybody knows more, please share here. My logic guess (besides those 3 attacks just being some kind of roleplay thing) would be that each attack has a slight advance over one of the others, kind of rock-paper-scissor style, but there's defintely no 100-percent-win involved. We could rule that out during our tests.