Hi!
  OK, this is basically a gut check.

  The system I am making will use a modified version of Otherkind (I already checked with Vincent and he is cool with it).

  The idea is, you roll 3 dice and after the roll assign one to Ambition, Cunning and Protection. You compare those to a target number determined by your opponent and from that you get successes. Ideally, it is my cunning roll against your protection stat. My Protection roll against your cunning stat and Ambition vs ambition. So, if I roll Cunning 2 higher than your Protection, I get a +2 success and that is the base harm you take. there is more to it than that, but this is a good overview.

  So, its is a game with Regular People (tm), magic, superscience and vampires.

  I want to allow players to add +1 to some dice and get bonus dice as needed.

  I ran the numbers and it looks like:
Bonus to one die - Increases the overall average number of successes, but does not increase the chances of getting successes on all three dice as much as bonus dice do.
Bonus Dice - They increase the likelihood of getting successes on all three dice, but does not raise the average number of successes as much as getting a bonus to one die does.

  So, what I want to do is assign one mechanic to mundane things (skill, traits, etc.) and one mechanic to kewl powers (magic, superscience, vampire powers, etc.).

  My gut tells me that acing all three dice is more "powerful" than getting a higher overall average. While getting a higher overall average is more "skillful" than getting successes on all three dice.

  Does that seem logical? Are there mathematical anomalies I am not seeing?

Hi!
  OK, let me ask it another way.

  If you had a bonus die. And I offered to let you add a +1 to one die after the roll. And you hadn't rolled yet. Would you take it?