Two Plus Two Newer Archives - Stack size vs stage of tournament (hypotethical/discussion)

A friend of mine was explaining about a tournament he was playing and explained a hand which happened on the bubble where he had an average stack with around <15bb stacks and reraised an open-raise allin with KK, someone from behind him coldcalled(with 55) allin and the initial raiser folded.
Buddy made a point that it was a good thing the other guy folded because it was the bubble. I made a point that it was a real bad thing that the other guy folded because he had KK.
Then he made a point that at that point of the tournament he wouldn't want more calls than one preflop because that makes it more likely he will bust, but also said that he would happily take four or five callers in the first level with KK. I made a point that its actually better to get more callers when you have KK late in the tournament because that way you have a big stack late in the tournament rather than in the early stages.
Now I'm not sure if its totally obvious but it seems to me that its way more helpful to have a big stack late in the tournament than in the early levels, even if you get double up multiple times early.
Which brought me to wonder about this fictional situation. Question is as simple as this:
You aren't forced to pay a bigger buyin or anything, but you get a bonus in the tournament or tournaments you play, you can choose from two options. Would you rather start the tournament with four times (4x) the normal starting stack OR have the option at any given point during the tournament (not during a hand) you have the chance to double (2x) your stack.
I havent thoroughly wondered about the situation so it might be possible that option B could be exploited in a sick way, but anyway pick your option, say why if you want or say why either option is superior to the other. Its a simple poll but I think it makes you think about what sort of tournament player you are and might result in some sort of enlightement. Or not.