When dealing with exhaust, I use heat to try to prevent breaking bolts or studs. If they are already broken, the best way I know to get them out is to plug weld a nut onto the broken stud. The process of welding a nut to the broken bolt usually breaks the rust loose. If it is broken too deep in the hole to weld to, drilling and retapping is usually the only option. If you use a bolt extractor, you risk breaking it off and it will be just as hard as your bits.

I prefer using studs over bolts for any kind of exhaust. That way I can heat the nut and it will come off.