criterion for the best fitting model if using GMM?

Hi,

I have two big datasets:10,000 observations and 40,000.

I tried to use ML so that I can use maximized LL or AIC to decide the best
fitting model! However it took so long and most of the time R was turned
off automatically.

GMM seems like a better option. I searched the literature but cannot find
the criterion for the best fitting model. Any idea?

thanks,

Chelsea