Def both. I'm pretty sure it takes a certain amount of both passion AND crazy to cut your own ear off and give it away as a love token.
*ahem* I'd say he was passionate for sure. Art was literally his life - it's what he lived for.
All things aside, though, he really WAS crazy. He suffered from arsenic poisoning, which resulted from ingesting the oil paints that were used way back in the day. It wasn't done on purpose at first, it happened when he (and many other artists) would hold brushes in his mouth while painting. He became addicted and later would actually DRINK his paints, and it made him batshit.
Still, he was always a little... different.