2nd type is little better.
Got to remember that those type extractors will EXPAND the stuck stud and make it get tighter as it's turned as the sides of the stuck stud are thinned.
Sometimes like mentioned in post #5 you can ALSO drill a hole into the twisted off stud, weld on a additional counter sunk stud so as to extend it's length for the nut to be added and then weld on a nut then peck hammer sever times BEFORE attempting removal. If you cannot weld into the center of the nut only try the The heat from welding also helps loosen the broken rusty stud. You were lucky it's not worse, like for example into a automotive block and the engine needs pulled to attempt removal/repair. (how do I know this)
But in this case just drill/tap for another bolt and move on.