
Notch-jaw pliers have a simple but effective modification to aid gripping. The cuts in the jaw grip from above, locking on to the corners of external drive heads and dig notches into the circular shape of gouged internal drive heads. You even have a chance with a sheared shaft as long as it's bigger than the notch.
Vampliers® (fangs for extracting that screw...)

Screw Removal/Extractor Pliers (Mole Grip Style, 185mm) with Unique Non-Slip gripping Jaws for The Easy Extraction of Damaged/Stuck Screws. ENGINEER PZ-65...
5.0

Gripping Pliers / Screw Extractors (non-slip jaws for quick removal of damaged screws). Made In Japan. Engineer pz-55 neji-saurus , Green
4.0