If I may caution you: Unless you are willing to wait for a l-o-n-g time, a general rule of thumb for someone that likes their jail break is - do not update/upgrade your iOS until a jail break for that iOS is actually released.
There is much good news about winocm's efforts, but he has stated he is no where near a release. And - there is no guarantee that he WILL release a jail break for iOS 6.1.3/4. And, so far, from what I read, he is having difficulties with support for all the different iPad models.
Therefore, my suggestion is to stay at the current iOS you are on and watch and wait. If a jailbreak is released for iOS 6.1.3/4 before Apple closes the signing window for that version (which will be shortly after iOS 7 has been released), then yeah, upgrade to it and jail break that version.
The key is, IMO - wait.
[/unsolicited advice]
Marilyn