Geek method - doesn't hurt, the pain is all acting. Wayne was completely comfortable the entire time and has had himself setup up to 4 hours beforehand, ready to perform. While pulling the thread from his eye, he talks naturally and normally, going over the routine. Might be uncomfortable for you, but as long as you don't yank the thread out or dig around your eye or something weird, you shouldn't be in pain.
In this method, you can open your eye and show the thread coming from it. In the sleight method, you can't exactly do that.
Sleight method - requires the tiniest of gimmicks, and it's probably not what you think. Not as clean and open as the geek method. Your gimmick will take less than five minutes to make and shouldn't cost much.
To us, they don't look exactly the same. To the spectator, they look very similar.
Geek method: swallow thread, pull it out (with the thread-in-mouth flossing action), show eye open if you want.
Sleight method: swallow thread, pull it out (with the thread-in-mouth flossing action), keep eye closed a bit, probably have to put your other hand in your eye for a bit depending on how good you are, and definitely at the end.