Can I switch two door frames?
Assuming these doors are exactly the same size, you should switch the doors by unscrewing each door's hinges from its frame, and then reinstalling in the other frame. You will probably need to mark the outline of the hinges in their new positions and carefully countersink the outline with a sharp wood chisel. You will need to switch the strike plates as well, to the other side of the frame, so that the door can latch. You may be inclined to touch up the holes left behind when you remove the strike and the hinge screws - I would use wood filler for the strike hole and wood filler/spackle for the hinge screw holes. 

You can remove and switch the frames, but that involves removing and later reinstalling the casing from both sides, and cutting the nails attaching the jambs. And unless the frames are exactly the same size, you run the risk of one of the rough openings being too small for the frame, which is a headache even if you are a professional. There are additional disadvantages if you are considering doing this with exterior doors (siding may be disrupted). If you do go this route, you will need to ensure the hinge jamb is installed plumb and straight (using shims behind your nails), and then ensure the reveal around the door is even (again using shims behind your nails in the strike jamb).