"(을/를) 못해요" 하고 "하지 못해요" 은 달라요? 어떻게 달라요?
I think the two are the same as far as the connotation goes.
The shorter 못하다 is preferred in conversation and ~지 못하다 in more formal, literary contexts using long-winded style.
Also, in some cases one might be preferred over the other because of surrounding structures which might make the other more awkward. I can't think of a good example of that off-hand but there are situations that make one of them work better than the other.
Same goes for 안 하다 vs 하지 않다.