black scholes - How do different models impact option Greeks?

If I trade an option using delta, vega, Prob OTM, etc. these are derived from a model. How do leading models impact valuations in terms of the Greeks?

I suppose to form a baseline it would have to be relative to Black-Scholes.

CRS Process Model, Heston Model, [CGMY][1] Model. For example, does the Heston model generally depreciate the delta of a call option relative to what BSM would predict? Can any descriptions of the models be learned from these comparisons?