Evani0n - this is the new tool for iOS6.1 jailbreak.
Here is link for download -
evasi0n-win-1.2.zip
As long as jailbreak available for iPhone 4, flashing Verizon and Sprint iPhone 4 over different networks available as well.
Currently 6.1 supported by one tool only:
iDFS Tool -
iDFS - iPhone 4 iPad 2 programming flashing tool - Flash iPhone 4 and iPad 2 easy