In my experience it should not make much or any difference.

I had devs try to "optimise" the JSON our services were returning by doing things like abbreviating field names that were repeated very often or replacing long string constants with short integers or removing formatting, and so on. When I asked them to do actual test when the service returns gzipped output and they found out that even reducing the JSON size this way by half does not make any measurable difference on the compressed stream in most cases.