Some reactors can also more effectively let xenon escape. That is one of the reasons why Alvin Weinberg wanted a liquid molten salt reactor, you can let the xenon bubble out like CO2 in a soft drink.
And if you do that, then the 137Cs ends up in the off gas storage rather than in the molten salt. A good fraction of the fission products escape the salt, which kind of shoots down one of the main selling points of MSRs.
https://gain.inl.gov/SiteAssets/MoltenSaltReactor/Module2-Ov... (see slide 23)