Sympathy is a synonym for pity, which I definitely don't want. I imagine cancer patients don't want pity either. Perhaps the word you were looking for was empathy - which is the ability to put oneself in another's shoes, to understand the struggles of another.

I agree with the above posters that those with cancer are seen as blameless (aside from lung cancer, as mentioned above), while those with mental illness are often seen as the creator of their own problems. I disagree with this, of course, but it's hard for outsiders to truly understand what we go through. From the outside, it may look like self-pity unfortunately.