Generally speaking, you could either apply a Mantel-Haenszel test for whether the impact of the exposure factor differs between groups A and B (basically a stratified chi-squared test), or almost equivalently, model with Poisson regression and include an interaction term between exposure and group status to test whether these differ.

Wikipedia is (for once) not very verbose on this subject, but does give a two-liner summary. http://en.wikipedia.org/wiki/Cochran%E2%80%93Mantel%E2%80%93Haenszel_statistics

Generally speaking, you could either apply a Mantel-Haenszel test for whether the impact of the exposure factor differs between groups A and B (basically a stratified chi-squared test), or almost equivalently, model with Poisson regression and include an interaction term between exposure and group status to test whether these differ (EDIT: I mean whether exposure differs by group here too)

Wikipedia is (for once) not very verbose on this subject, but does give a two-liner summary. http://en.wikipedia.org/wiki/Cochran%E2%80%93Mantel%E2%80%93Haenszel_statistics