Git for Windows uses MSYS, which is actually a fork of Cygwin. Compared to Cygwin, Git's MSYS distro is missing a lot of software and the version of Vim packaged with Git for Windows is a native Windows build (not MSYS-aware,) so it doesn't work in mintty. This can really bite you when editing a commit message or trying to do an interactive rebase. On my machine, Vim will just hang when started from an MSYS mintty.
Then Git for Windows (which is built upon MinGW, and includes bash, grep and whatnot) + MinTTY is immensely more useful and lightweight than Cygwin.