It would obviously be Norris. The Stig is only known for driving fast, never speaking, and doing weird things. Not once has he ever been known as invincible, & if Top Gear are anything to go by, they already retain the ability to kill him off at will. In fact, they just did & brought in a new one.
As for the argument they are the same, they can't be. Top Gear wouldn't be able to bring a "new" one in so easily unless the farm of new Stigs is actually a farm of Chuck Norris' & there is simply only 1 Chuck Norris.