It's not an either/or. It's often both. 11% of the homeless population is US military veterans [1], often returning home with undiagnosed or untreated mental illnesses. They're failed by our healthcare system (same as opioid abusers) and sent out onto the streets. I'm sure there is significant overlap with prescription drug abuse and homeless veterans as well.

[1] http://nchv.org/index.php/news/media/background_and_statisti...