We can make fission plants that are also immune to run away reactions. Even with old designs, you have to do something really stupid like have nightshift take out all your control rods to get a run away reaction.
While the fusion reaction itself isn't very dangerous, the magnetic coils in a fusion reactor can potentially quench, causing them to explode, which because of their position will throw radioactive debris from the irradiated reactor vessel all over the place, as well as your tritium breeding blanket which will be highly flammable, toxic, and a bit radioactive. Worse, you can't make the magnets passively-safe.
Then there are the standard issues like tritium release. And you have nuclear proliferation concerns as a fusion reactor is great at making plutonium by just doping the tritium breeding blanket with some natural uranium. In fact, the first "fusion" reactors will probably do this anyways as they need to produce more tritium to get more reactors online and because this dramatically increases power output - so you get all the fun of dealing with fission products too.
I would be willing to bet complying with the safety standards for fusion will in fact be more expensive than for fission. Yes the general population doesn't have the same irrational fear of fusion that it has of fission, but once people start seriously proposing to put these in people's backyards that will likely change.