What determines the differences in results between various weather models? It's often said that the ECMWF model is more accurate than the GFS. But what are the reasons why? Also, how does the NAM compare with these two and other forecasting models?
Everything.


Parametrizations
Spatial (horizontal and vertical) and temporal resolution
Initialization
Dynamical core
Handling of some complex non-linear physical processes (i.e. snow)
Topography representation
How the mathematical equations are numerically implemented
The computer used
etc...


These are some of the main differences between 2 given numerical weather model. 

With that being said, the same model will give different results when run on a different computer (Hong et al. 2013).

Hong S-Y, Koo M-S, Jang J, et al. (2013) An Evaluation of the Software System Dependency of a Global Atmospheric Model. Mon Weather Rev 141:4165–4172. doi: 10.1175/MWR-D-12-00352.1