If you have to play with neutrons, fission has the advantage of being surrounded with water. Fusion needs a vacuum so it's hard to stop the neutrons and absorb their energy.
In the case of the tokamaks, where they are trying to put helium between the cryogenic-cooled superconducting magnets and molten lithium, that may be a significant problem. However, in the case of Polywell, not all neutrons hit the grid, depending on what coil-configuration is used.
That means that neutrons are free to fly into a wall where their energy can be absorbed by neutron-killer material. I recall that for the neutron-based Polywell, boron-based components would be used, as they are the most potent neutron killers.
In tokamaks it's called the "first wall" problem, and if you are going to use DD or DT in an IEC device you have the same problem.
The problem of shielding the device is there, however due the reason mentioned before (that the electromagnets are in there in the form of coils, and are not the reactor room and reactor itself), this problem is different. Also, I think Polywell doesn't need to produce tritium (if tritium is used at all) in-situ.
There are however, to my limited knowledge two main issues when it comes to simple fuels with fusion: the neutrons destroying the reactor/magnets and cooling.
In the case of fission, there are no need for magnets or anything, the fuels themselves produce reactions, one merely has to control it with control rods. The control rods require nothing else but (relatively) simple mechanics.
As for cooling, the magnets have to be cool in order to provide a sufficiently powerful magnetic field that would (in the case of Polywell, indirectly) produce fusion. In the case of fission, cooling is what gives power: that's what the thermal cycle is about. However, getting rid of the grid's waste heat is a much more difficult task.
For fusion to beat fission in terms of economic viability it will have to go aneutronic. Otherwise you get just as many radioactive buildings and components even if you don't have radioactive fuel. The problem of radioactive fuel has been solved for fission with metal fuels and breeder reactors.
Not quite. The waste produced by fusion is much lower half-life and radioactivity, although this very much depends on what components do the neutrons hit.
Dr.Bussard also has ideas of using neutron-based fusion. Look at the video at 59:00-60:00.