Both these modules do the same thing: add gzip compression on the fly.
The one you should use these days is mod_deflate – it is the more modern and recommended one and is distributed with Apache. mod_gzip was an older third-party implementation and there is no good reason to use it anymore.
Don’t be fooled by the names into thinking they use different compression schemes. They both use gzip (which is a format that uses a compression algorithm called DEFLATE). The latter is only called mod_deflate because the name mod_gzip was taken. They both will achieve the same compression levels with equivalent settings.
They have different configuration (which may include different default settings) so you need to find documentation for the specific one you’re using.