It doesn't matter if you used Greenpois0n before because Sn0wbreeze like Pwnage Tool does a total reload of the OS. I'm saying this for anyone who tries to help you they will tell you to reload the OS fresh. So what I would do first of all is list for us what you're settings are because many people are quick to blame the JB when it's something they have installed or a setting they have.
What is the brightness level of your screen?
Do you use push or fetch for your emails?
How many email accounts?
How often is the push/fetch interval?
Do you have OpenSSH installed? Do you turn it off when you're not using it or you reboot the phone?
Do you leave Wifi on when you don't have Wifi coverage?
If you answer those questions and you can't find anything that could be causing this issue then you can remake the custom ipsw with Sn0wbreeze and do a reload of the OS to see if it's any better. If not then do another reload but finally setup the phone as new instead of restoring from backup. This means you will have to setup everything all over because your settings, wifi places, game save data, text messages, etc. will all be gone.