The kanji make me think that the first is like surviving (through something difficult) while the other is more like surviving (when others didn’t).
A native Japanese friend confirmed that, to her, the first one would indeed imply surviving through something extreme (such as war/apocalypse, like a cockroach). When I followed up asking about the second, she said she felt like it would mean essentially the same thing to her as the first. Just curious if others would think about this the same way!
by trittik