  We consider a Cahn--Hilliard model with kinetic rate dependent dynamic
boundary conditions that was introduced by Knopf, Lam, Liu and Metzger (ESAIM
Math. Model. Numer. Anal., 2021) and will thus be called the KLLM model. In the
aforementioned paper, it was shown that solutions of the KLLM model converge to
solutions of the GMS model proposed by Goldstein, Miranville and Schimperna
(Physica D, 2011) as the kinetic rate tends to infinity. We first collect the
weak well-posedness results for both models and we establish some further
essential properties of the weak solutions. Afterwards, we investigate the
long-time behavior of the KLLM model. We first prove the existence of a global
attractor as well as convergence to a single stationary point. Then, we show
that the global attractor of the GMS model is stable with respect to
perturbations of the kinetic rate. Eventually, we construct exponential
attractors for both models, and we show that the exponential attractor
associated with the GMS model is robust against kinetic rate perturbations.
