I think it would cost more than a billion dollars in order to own an entire planet. If that was the case I would either be drowning in debt or earning income from my planet. Unless I had to pay for the problems too such as alien attacks, in that case I wouldn't like it. Not to mention all of the blame I would get for things and the extraterrestrial terrorists that want to kill me because secretly I'm trying to conquer the universe and it's up to one heroic man, J. Spaceman, to defeat me and rescue princess Starry in order return peace to the universe! Coming in 2030!
So to answer the question... I would take the billion.
You may not believe this, SushieBoy, but I've actually seen a book with this exact topic. "Would You Rather..." It's just like this except the questions are much better (no offense to anyone) and are meant to make people start talking about interesting thing. I think this topic would be even better if we asked questions like that and had more to talk about. That's just my suggestion and you don't have to do it.
Would you rather... have a big nose or a big butt? (an actual question from the book)