LFTR would be far better. Neutrons breed new fuel, and it consumes virtually all the radioactive fuel with "waste" that rapidly becomes non-dangerous within a month.
So I would guess neutron degradation of the equipment/vessel/reactor will probably be a similar problem in both cases.
IIRC people have stated that the breeding could also reprocess the bad millenial-scale waste from LWR into usable fuel or other isotopes in MSRs, although maybe not in LFTR.
If we had a decent LFTR industry, we could probably have more specialized MSRs to deal with the "legacy" waste and breeder reprocess into new fuel or other stuff.
The chemists from ORNL seemed pretty amazing. They had all the work done for separating out the byproducts for use in other applications.
I wonder, how can this possibly be even a question? Fission based reactors obviously have the same or worse problem of irradiating the entire reactor enclosure and everything around it, so that's at best the same as a fusion reactor + they produce tonnes of very highly radioactive waste that will be radioactive for millennia.
Materials activated through neutron bombardment aren't radioactive for anywhere near as long. And to add to that, nearly all elements produced in a fission reactor are highly toxic in addition to being radioactive - in a fusion reactor if your steel containment chamber becomes activated, you just have radioactive steel, not one of the many many dangerous heavy metals produced through fission.