My initial thought was that vessel B would exhibit slower rate of diffusion and/or have an equilibrium shifted more toward the chamber initially containing sodium chloride, in order to equalize the total number of ions in both chambers. However then I convinced myself that maybe this is not the case, that a high ionic strength solution is "more polar" and solubility of additional ions would be favored, such that vessel B may have the faster rate of diffusion. Now I can't decide which is more likely to be correct. :/
This does have some relevance to something I'm doing - I have some experimental data that suggest the first scenario may be the correct one. Well, anyway a high ionic strength in a solution reducing an ion diffusion rate was a hypothesis I created to explain some experimental data, but then after thinking about how ionic strength affects the solubility of solids (actually making them more soluble) I'm not sure. This is why I created the thought experiment... but it turned out not to be helpful because as mentioned above, I can talk myself into either answer.
Obviously it's hard to create a magic membrane like the one described, but I wonder if there's a more realistic system that could be designed to figure out the answer.