Personally I think I'd choose invincibility. The idea of going to a buddy's house and telling them to shoot you while you watch they're jaws hit the floor sounds very endearing. Think of the possibilities...
1) Joining the military for a free education and bonuses, then going over to where the actions at and absorbing bullets and ripping your Anti-(Insert Country's Name Here)'s a new sphincter. If you start young, by the time your 25 you can retire.
2)You'd be able to make excellent slapstick humor. Imagine going up to a girl and saying 'Babe, check this out,' and walking in front of a speeding bus, then getting up and buying her a mojito. I'm totally nominating that for best pick up line.
3)If somebody annoys you, pick a fight and then fall under a bus and take him with you. Miraculously you survive but...Him? Not so much.
4) I don't know about you guys, but...Parachuteless Base Jumping FTW!
Besides, if anyones read 'Interview with a vampire', they would see the rather creative and frightening way the author describes immortality. If you were born in the 1600's and suddenly it's 1936 and the police drive down the street with these blaring red and blue things, you might not be able to adjust. Old people talk about the good ol' days and die for a reason. They can't cope.