I see where you are coming from but most fallout isn't from the leftover nuclear fuel (that would be a tiny proportion of the fallout).

Similar yield fission and fusion bombs might have different fallout characteristics. I think pure fission bombs would have some degree more deadly fallout due to increases of Strontium 90 and Iodine 131. Both of those elements would be a concern even in very small concentrations.

I will be honest this is just a hunch, but it seems reasonable.

Most Fallout is created when the fireball touches soil the sudden neutron flux interacts and creates isotopes also the higher yield devices are a 3 step process fission fusion and a secondary layer of U238 to increase yield. Similar to the isotope creation except it's high speed fission they're after.