Your numbers are tautological. Everyone including your straw man vc would take 10% of 100 instead of 0.1% of 1000. 10 > 1, qed, but you don't get any points for that observation.

(yes, there are situations where taking investor capital leads to divergent interests between investors and managing founders. But not gross arithmetic differences.)

Obviously if the expected value of the smaller sized business is greater, you choose that one. The only time these questions (whether to take capital/shoot the moon) is when the expected value of the larger business is greater. So to refactor your example, what about 10% chance at 100, or a 1% chance at 2000? Now you have more of a real question on your hands.

Much more interesting when contemplating whether to go big or stay small is the notion that there are invariant personal "fixed costs" regardless of the size of the opportunity you're pursuing. Meaning, you can overwork yourself and burn out on a $100k/year business as surely as a 100 M/ year business. So if you are going to give something your all, just make sure the expected payoff is worth it.