Whenever something is in one house by one system but another house by another... like 12th whole sign but 11th in whatever quadrant system you use... I like to look at where the meanings of the houses overlap. Adjacent houses always have some common ground. I think that also works well for planets that are right at a house cusp.
In the case of your sun, both the eleventh and the twelfth houses deal with the long term, the future, who you become to your society, what you will be remembered for, and the legacy you leave. In the eleventh live people who help you get there (a more archaic meaning of the word "friends"). In the twelfth live the influences you don't necessarily know... what you've inherited from ancestors gone before you were born, the secrets that died with them but that you might still be living out in your own life, that kind of thing. For someone whose sun straddles those houses, both the real world community and the unseen community are key growth arenas.
I have the same Mars house conundrum: Mars is in my sixth sign from the AC, but right on the cusp, so every system except whole sign places it in the fifth. I see a need for passion and movement in my work. I'm not at all content with sitting at a desk all day, week after week (Mars in Gemini!). If I like what I'm doing, I can keep it up for a while, but if I don't, no way is it going to last.
The fifth and sixth houses share the meaning of "what you do." In the fifth house, you do things because you want to. In the sixth, you do them because you have to. Ideally, what you do for a living (or day to day, if you're not employed for pay) stems from what you truly like. Perhaps a driven Capricorn Mars would have you turn something that you've become good at because it was your hobby, and you were motivated to do it until you perfected your skill, into your job. If you're crazy driven at work, maybe you've done just that, or maybe you've found that you like your work, and/or the rewards it brings, which motivates you to keep being driven.