I am trying to compare a SW part that I recreated to the original using the SolidWorks Compare Utility. When I do the geometry compare it makes me select which coordinate system to use. I cannot figure out how to line up the two parts so the compare geometry actually works. Is there any way to fix this problem or a different way to accomplish what I am trying to do?

If the Global Coordinate System for the two parts is different, I would just add a Coordinate System to each of the parts, so that they will be in the same place.

Reference Geometry -> Coordinate System

Pick your X,Y,Z

Repeat for the second part

Then you can change how you align the parts to the new coordinate system in the "Compare" dialog box.

(In this example, I created the two parts different, but I made the new Coordinate System from one of the parts match the Global Coordinate System of the other part.)