MinGW supports only 32 bit binaries, TDM supports 32 and 64 bit binaries (with usage of MinGW's API's).
- If you need a good GCC for Windows, with the drawback of 32 bit only, use MinGW.
- If you want to build 64 bit binaries too, you can use TDM.
Both released GCC 4.8 approximately at the same time, so there's no real difference in up-to-dateness.
My recommendation: Use the 3rd alternative: MinGW-w64 instead - it's a extended MinGW with support for 64 Bit. See here for a short description of MinGW-w64.
Whatever choice you make, better use official developers website for downloading (not Orwell's) to get most up-to-date version.
Btw., you'll find a good overview there, what makes one special about the others.
NB: the homepage of mingw-w64 used to be on sourceforge but is now at http://mingw-w64.org ; links have been updated accordingly.