I've hear some good and some bad about the gator grip. The bad is those little pins have been know to break. I personally use Craftsman bolt out for bolts with heads and screw out with bolts that don't. But that is just one opinion.
One of the Bolt-Out sets would probably do a better job on removing a stripped nut or bolt head.
However, unlike the Alligator Grip socket tool, a Bolt-Out Extractor is a destructive extraction tool that will often require the replacement of the fastener it extracts.
I have had a lot of luck with vise grips. Also a chisle. I make a groove in the nut, then keep tapping it till it breaks free. Ill have to buy some of those special sockets and try them out.
That 3/4 inch electric drill, about broke both my arms when the twist drill bit "snagged" on the pilot hole.
Now, I know why they have that piece of threaded pipe as a side handle - to bury into the ground, pavement or on the cement floor BEFORE turning the beast ON!
That method works great when you've got access to some form of welder and the area you're working in has a combination on non-flamability and no plastic parts that could be damaged by the heat of a welding operation.