Hi Rick--

Another angle on how closely the two are related is shown in our entry http://sas-and-r.blogspot.com/2011/03/example-830-compare-poisson-and.html, where I demonstrate that the cumulative probabilities for the negative binomial approach those from the Poisson, as the size increases.

I now default to using negative binomial models for all count outcomes, as it seems the cost (1 additional DF) is small and the benefit of the additional flexibility is great.