Plumbing. If you want to add a bathroom in the basement, find your soil stack and see whether the main drain for the house goes underground or runs aboveground. If it runs underground, as long as you put the new bathroom near it, plumbing shouldn't be much more difficult than upstairs.
If it runs aboveground, you will most likely need a grinder and a pump — like those made by Saniflo. Water runs down via gravity, so if you want it to go back up after you flush, it takes special equipment.