Does a table summarizing basic details of significant operational weather models exist?
MetEd from NCAR has a good encyclopedia of models that summarizes some weather models. Of course, when models update, such as the GFS dynamical core being converted to the FV3, or changes in data assimilation systems, they may not be up-to-date. This also doesn't have ALL weather models, but some of the more common ones.

Of course, there are models missing from the encyclopedia, such as the SREF, GEFS, the JMA model, the Panasonic weather model, any iteration of the WRF model, statistical post-processed models, etc.