It really is a poor idea to start PCs at different power levels. You're going to have some people taking all of the screen time and others simply fading into the background. There are some ways to have differently powered characters in a game and I'll use the same example that you did: Harry and Butters.
Were the two of them PCs in the same game you would likely have harry, a wizard with all the powers that implies and a broad skill set able to do magic but also investigation, shooting, intimidation, etc (lots of powers, little refresh and a broad skill pyramid with the highest being great). Where as Butters would take a different appraoch, being very good in a few skills and having a few stunts but a lot of luck (a couple of stunts, A LOT of refresh and a very restricted skill tower with the highest few being superb). I'm sure this isn't necessarily how they are stated but it's how I would do it were two people trying to create these characters in a game.
Well, Butters is a fairly extreme example. Not all mortals are a 2 refresh like Butters more than likely is/was.
Polka trivia is not that relevant to fighting evil.
That said, I think a were-tiger or other powerful were person would be able to hold their own. Being able to switch around skills and have natural weapons is a rather awesome power. Plus, animals are /fast/.
I also like the idea of people who cannot throw down with another PC against a mob toe to toe being able to sneak around and do more intelligent/sneaky things.
For instance, I've Larped and in my group once was a kid who had no real fighting ability in RL, and no real fighting skills either. He had no real armor of note and sunk all of his skill points into non combat skills.
However, the kid was good. He was able to broker deals with NPCs, he stayed in character pretty well with a very mysterious past, and he was sneaky as hell. He killed as many people as some of our other more "in your face" players.
Using the book as an example again, Harry rarely goes toe to toe with folks more powerful than he is. He uses guile, proper planning, and a little help from his friends. I think that having characters with different power levels will be interesting.
As powerful as a high level evocator is, she may still be terrible at lying or noticing details. This is where a con man vanilla mortal could shine. In fact, in some groups, the character with the lowest refresh could be the leader while the higher level characters function as muscle.