Testing in one model would be done by simply adding an interaction term. A significant interaction term would show the slopes are different.
If you're testing across two models you could get the confidence intervals of each slope in each model. Then, use those to infer whether the slopes are different. With R and the lme4 package, if your model was
mc <- mcmcsamp(m, 1000)
will get you confidence intervals of your slopes (all fixed effects actually). This only works for fixed effect of slope, not random.