In my experience, anapana is more difficult and brings up more stuff because, unlike vipassana, simply focusing on the breath doesn't provide a way to deal with the stuff that comes up.

Hm, what does 'deal with' mean here? To me it brings to mind 'apply rapid fire cognitive behavioral therapy techniques', but that would require conscious deliberation on the thought. Perhaps the difference is that anapanasati is (or can be) just concentration where vipassana is concentration and mindfulness, and only the mindfulness part helps in dealing with stuff that comes up?