How is global weather model skill measured?
There are lots of articles that assess global models both locally and globally. They usually focus on a few parameters that are easily comparable with observations (e.g., temperature, wind, surface pressure). A couple of examples of the many available: 


for ECMWF:

Roberto Buizza, 1997: Potential Forecast Skill of Ensemble Prediction and Spread and Skill Distributions of the ECMWF Ensemble Prediction System. Mon. Wea. Rev., 125, 99–119, doi: 10.1175/1520-0493(1997)125&lt;0099:PFSOEP>2.0.CO;2.
for both only looking at precipitation:

Thomas M. Hamill, Renate Hagedorn, and Jeffrey S. Whitaker, 2008: Probabilistic Forecast Calibration Using ECMWF and GFS Ensemble Reforecasts. Part II: Precipitation. Mon. Wea. Rev., 136, 2620–2632, doi: 10.1175/2007MWR2411.1.
For the climate model world, check out: http://www-pcmdi.llnl.gov