It seems trivial that it's better than option 1; in both cases a mentally ill person is flying the plane, and in one of them a health professional is involved in managing the condition.
For option 2 I'll confess to not being sufficiently familiar with the gamut of what can be considered a mental illness, such that I couldn't tell you whether a person under management for such is a safer pilot than someone undiagnosed, or the median pilot. I'd be mildly surprised if you were, but stranger things have happened.
As it stands, I expect these would be the same diagnostics that until ~2013 considered sexual preferences as mental health issues.
