You can use both sets of outputs together - plugging into one pair does not mute the other pair. However, you cannot send different output signals over the two pairs. In other words, the signal you send out of both pairs will either include the cab/mic simulations (STUDIO mode) or it won't (one of the LIVE modes).

Ideally you'd like to send a STUDIO signal to the FOH and a LIVE signal to your power amp. I believe there's a way to do this that involves the FX Loop but I don't have personal experience with it. You can search other threads for this approach, or perhaps another user with experience in that area can chime in here.