I would like to compare two beta coefficients from two different Poisson models which have the same variables and applied to different samples. I would like to test their difference to check if the null hypothesis that their difference is zero can be rejected. Both models run on a sample of size N=120. A similar question has been posted here for linear models: Test a significant difference between two slope values
$$ Z = \frac{b_{1}-b_{2}}{\sqrt{(SEb_{1})^2+(SEb_{2})^2}} $$
I am wondering if the same approach (z-test) can be used also in this case. Also a bit confused because z-tests assume knowledge of the population variance which we don't have either in my case or in the example. I presume it is based on assuming an asymptotic standard normal distribution under null hypothesis? Would a t-test be a more appropriate choice or some other test?
I understand that making one common model and having an interaction term would also answer this but i would like to know the appropriate way to test this when having two different models.