Thermonuclear bombs are orders of magnitude more powerful in terms of blast and radius of effect than purely fission devices but the residual radiation in the form of fallout isn’t necessarily greater in proportion with the increase in blast effect. The fallout radiation comes from unconsumed fissile material and fission byproducts like cesium and radioiodine. Fusion doesn’t produce radioactive byproducts itself.
Boosted fission weapons (fission-fusion-fission) weapons might be a different story. I don’t have any information on fallout from boosted fission weapons but the secondary fission “spark plug” might be expected to create additional fission products.
A big variable in the production of fallout is the weapon height of burst. A graze (surface) or subsurface burst sweeps up huge amounts of soil and ash that are mixed with fission products. Air bursts, where the fireball doesn’t touch ground doesn’t yield anywhere near the amount of fallout while simultaneously vastly increasing blast and destruction through the Mach stem effect.
Thank you for that info.