Obviously, なきゃ is the short/casual form of なければならない like in: 病院へ行かなきゃ。 I need to go to the hospital.
But I've also seen negative + と be used to express the same thing. 病院へ行かないと。
I assume と here is conditional but is a difference in nuance between the two? Or are they both interchangeable?
Simply, ～しなきゃ is more informal. It is usually wise to avoid しなきゃ unless you're talking with your friends (although this depends on your age and personality). ～しないと is not particularly formal, but it's polite enough when you are conversing with a stranger or your boss.
More generally, the eba-to-ya contraction is considered highly colloquial or informal.
