I tried quasi-poisson and negative binomial glms on my counted data in R. The estimates are pretty much the same but p-value are different. Quasi-poisson gives insignificant result. NB give significant result. I am not sure how to decide between the two models. I computed QAIC for quasi but I read a paper saying that it is created to compare within quasi family. Another one says we should compute to compare with AIC. Is there any other way to compare the two models?
Quasi-poisson NB
Deviance/DF 994.93 3.0014
Person chi-square test 995.64 2.997
QAIC/AIC 5.041 68.47