I have been able to change the storage options for the camera (e.g. from internal storage to external SD). However, I have no idea how to change that setting, or even control in which format the screenshots are saved. Moving the "screenshots" folder to external storage manually had no effect.
I have Jelly Bean 4.1.2.
You can achieve this using Foldersync app.
Add folderpair and select account: SD CARD. Then you can select source by finding your screenshot dir and select target dir on your SD.
It also has full range of advanced options if you don't like how default options work so everything is covered.
Bonus tip: this app can also do backups of your SD (or internal) card to remote storages such as Dropbox, Google Drive, Owncloud, etc.
I don't think you can change this in your phone settings. If you are interested in third party apps then try this app Screenshot and this app Screenshot
Note: Both are different links.