I need to compare the results of two computer simulations in order to establish their equivalence. Each simulation result (actually it is the average mean count + variance over multiple simulation runs) is a group of counts and I am aware that the chi square test of homogeneity is a possible way to go. However, while the counts across the two groups are independent (one simulation does not affect the other), the counts within groups are not (completely) independent. For instance, the entities being counted interact during the simulation and so a higher count of one type of entity potentially affects the count of another type of entity.
My question is whether the chi square test of homogeneity is still applicable in this case and, if not, what other test should I use to compare the count distributions in both groups for equality.