I use both cygwin and msysgit. Cygwin provides 64-bit binaries for git, but it's UNIX compatibility layer sometimes causes problems with the files when they are in the working copy. A problem I have hit is if I had an ".exe" and a file with no extension (for UNIX) in the same folder with the same base name, it will say the file already exists.
I use the 64-bit binary primarily to do an
git svn clone of an existing SVN repository which had large check-ins at one point and the 32-bit msysgit binaries just don't work with it.
However, once I get the repository loaded, I use the 32-bit msysgit because it integrates with Windows better.