I am interested in the software Homer and would like to know whether I could use this software to compare the outputs of a vertical axis wind turbine (VAWT) and horizontal axis wind turbine (HAWT) of the same rating.  Could I use Homer to estimate the power output for VAWTs?

Yes, you can model vertical axis wind turbines in HOMER.  The default wind turbine library does not contain any vertical axis turbines, but it is easy to add to the library if you have the power curve data for the turbine.