Well you just have to ask xkcd about how hard shielding is to discover that actually shielding is really easy on earth. You only have a problem if what is supposed to be inside the shielding escapes. Fission is difficult to manage the radioactivity of because it produces two daughter isotopes with far too many neutrons between them, and so are probably unstable. They can be a huge range of different isotopes with varying chemical and nuclear properties and there is very little you can do to influence which are produced. They are not nearly as heavy as the parent nucleus, but they are not light, making isotope seperation difficult after chemical seperation. Many of the products are very good at stopping your reactor working well, meaning that your fuel burnup rate is very low without reprocessing, which in turn means that you produce a lot of medium level waste rather than a little high level waste. This is before you consider the range of transuranics that can be produced when a fission event does not occur.

These complications are inherent to fission, and cannot be avoided. With fusion the problem is neutron activation of the reactor. The reactor can be made of whatever we like, so we can influence how this occurs. For example, if we build it entirely out of carbon, oxygen, hydrogen and silicon, which could be possible, then the same atom has to capture two neutrons before any radioactivity occurs, and even when this does happen we only have to deal with a small range of radioisotopes. If an element is problematic under neutron bombardment we can just avoid it, so there are no inherent problems (though that won't stop us making some).

HEU reactors are used by the military because they can be made much smaller than a conventional reactor, with the down side being that you have to enrich the uranium to a much higher degree. This makes them far more expensive to run.

The safety thing is a bit overblown but actually not that much of a problem for fission. Public squemishness is a stumbling block, but the lack of a good solution to the waste is the real biggy. Personally I think we should fuse it all into silica and then put it in a big pile on top of a deep salt lake. Let it get hot, and melt it's way down, then install water pipes to use it as for geothermal power to offset the cost of fusing it into silica. It might take a few hundred years, but we should be able to recover all the cost of disposal that way. It should be pretty safe too, with the salt melting and convecting if it overheats, and there being no water for miles. That might just be the mad scientist in me though.