First, the radioactivity is spread through a much larger volume of material. The cost of dealing with it will have a component related to the volume rather than the total radioactivity. It's not clear that dealing with fusion's waste problem will be cheaper than dealing with fission's.
Second, getting low induced radioactivity, and particularly low production of radioisotopes with long half lives, may require expensively low concentrations of impurities in the reactor materials. For example, the RAFM steel Eurofer 97, a top candidate for a DT reactor construction, contains a small amount of nitrogen. Even this trace caused problems from 14C production pushing the steel over a regulatory limit requiring the steel to be disposed of more expensively due to that 14C content.
(I also have seen a claim from Abdou that the Eurofer 97 for DEMO would cost $3B, just for the raw steel. I'm not clear where this estimate comes from but it could be due to the need to expensively purify the steel of impurities to avoid their activation.)
The neutron flux produced by a fusion reactor will be much higher than in any fission reactor, and it must be absorbed in a shield, to produce heat, which will be the output of the fission reactor.
Choosing an appropriate material for the shield will minimize the quantity of radioactive material that is created per unit of output energy, but it is pretty certain that the radioactivity will not be "several orders of magnitude less".
The best that can be hoped is that it is possible to find a shield material that will produce only very small quantities of long-lived radioactive isotopes, so that, after a storage for not too many years, the radioactivity might decrease to be "several orders of magnitude less".
Nevertheless this remains to be demonstrated.
For example, any piece of steel present near a fusion reactor would produce copious amounts of cobalt 60, but that would decay to negligible radioactivity after a few hundreds years.
Moreover, to ensure the predicted low residual radioactivity, any shield material needs to be free of impurities, which even in very small quantities could produce dangerous radioactive isotopes.
The requirements for advanced purification will greatly increase the cost of the structural materials for fusion reactors. However this is not a new problem. Similar requirements are imposed on the structural materials for fission reactors, but the fusion reactors will not be any better from this point of view.