Is there a rule of thumb in English for which of two equivalent contractions to use [see examples]?

“It isn’t allowed” vs. “It’s not allowed.” Precisely the same meaning, two different possible contractions to use.
“I haven’t gone there” vs. “I’ve not gone there,” similarly.

In reviewing my writing, I’ve found that I naturally lean towards using the latter option, but I think most people would probably choose the former.

Is there any kind of standard for this? Does one or the other sound more “right” to you?