The thing that the Inquisitors use is something of a third magic system. Brandon has only vaguely referenced it in his annotations: it is called Hemalurgy. We don't exactly know what it does, but we have certainly tried here on the
Comprehensive Hemalurgy Thread.
I have theorized that, sort of like how the "body" burns metals in Allomancy, in Hemalurgy, the converse happens: the metals act as a sort of lightning-rod to "burn" the body's energy. That's the idea, distilled to the core. On page 7 of the Hemalurgy thread, I explain it much better (as long as I don't confuse you).
However, this not complete in any form. The creation of Inquisitors requires a lot of blood--we term them "blood sacrifices", generally. My theory doesn't even touch upon the relationship with Hemalurgy and Blood, so that is a major lapse. The truth is, we really don't know anything for certain about Hemalurgy. It's all logic and speculation, and at the time of theory, I had the inspiration to write about metal lightning-rods, essentially.
For all we know, the "thing" Hemalurgy burns is the blood itself (mind you, I say burn because it is a common Allomantic term. There is probably a better term Brandon would've used). Even if you use pewter, a crash will catch up with you. A pewter-dragging crash is probably even more acute for Inquisitors. Besides, pewter wouldn't re-create the blood, it just creates temporary strength. So, Inquisitors would be very powerful when they need to be, but they would also need to sleep a lot. Which is exactly what we see.
The second major lapse is the relationship with Allomancy and Hemalurgy. I can't even speculate to that one yet.
Anyways, I suggest you read up on that theory. I happen to like it, and even though it has flaws, I really like criticism. Small ideas often have a tendency to ferment in my brain into 3000-word theories, like this Hemalurgy one.