A friend of mine, who definitely enjoys her wine, was talking about a vow she'd made recently -- "No more hangovers!" And a funny thing happened: she was at a business/social event, drinking moderately, when she felt nauseous. She left the party, went back to her hotel room, had a glass of water and fell asleep, only to dream that she was milking a rattlesnake, symbolically pulling the poison from her system. And she hasn't had a hangover in the months since making the vow.
So obviously, vows can be powerful. They tend to be simple. declarative statements, structured in absolutes. Sometimes, they're stated in the positive, though they're usually stated in the negative, such as "No more..." They're often stated in the future tense, such as "I'll never... again." They are often stated in the third person, such as "This ____ stops now!" And they're generally made just once.
Affirmations, on the other hand, are positive, present tense, first person statements, which are repeated over and over till they become true. They're powerful, too.
So how can these two opposite ways of expressing a clear intention both be so effective?
My guess -- and it is just a guess -- is that an affirmation comes from a superficial part of the self, which desires change, while a vow comes from a deeper part of the self, which recognizes an internal change has already happened, and just needs to manifest in the exterior world. An affirmation is a declaration of what you choose, as if it already exists. A vow is a statement of what already exists on the inner planes, declaring itself to the outside world.