Well, first it would be good to compare boths. Can you make the git conversion
available somehow ?

One thing might explain mercurial conversion to be much larger: renaming of
large files. That would not be surprising given the number of branches and the
amount of binary contents. One possibility is the convert extension detects
rename incorrectly and duplicates files uselessly. Or this is a mercurial
shortcoming, see http://www.selenic.com/mercurial/bts/issue883 for details.

BTW, your 188MB is a bit strange because when converted under Windows or MacOSX
I ended with something around 300MB. That may be a case-sensitivity issue, I
will have to check again.