What determines the differences in results between various weather 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