I believe that brandishing a weapon is a very effective demotivator for the criminal in this case, but it definitely ups the ante as far as possible violent outcomes is concerned.
Generally, handgun instructors, home-defense gurus, self-preservationists say the best course of action is to keep any weapon you have concealed for as long as possible. When it becomes clear that the attacker is determined to hurt you, you respond with overwhelming and sudden presentation of force. It's the best way to 1.) hopefully not have to use force against an attacker - if they just take out a knife and say give me your wallet, you can just give them your wallet and they'll most likely turn and high-tail it (compare how much that costs you with attorney's fees and a trial for self-defensive homicide) and 2.) not be reactive as far as the use of force goes. Imagine someone pulling a gun or knife on you. Then you pulls yours. Then there's hesitation as you wait to see how the criminal responds. If you wait until you're reasonably sure of a will to use violent force against you, yes it's possible that you'll be completely unable to deal with their actions, but you can unambiguously act, which is 90% of the game.
This is what I've gathered from reading about self-defense... YMMV.