Tai chi is originally a martial arts practice; while qigong are exercises that focuses on the circulation of qi (for health benefits).
In some ways I would say that tai chi is about the application of chi in movement, and qigong is about focusing on chi for chi’s sake and the health benefits associated with it.
As a result, tai chi tends to have a larger range in movement—and if you learn it at the level of a martial art, demands strength, stamina, focus, and quick thinking. You also need to use the chi in movement, so that your force becomes pilable.
If you are trying to decide between the two, I would say: try tai chi if you want the physical exercise that goes with it; try the qigong if you just want the health benefits of chi, and just want something simple (i.e., don’t have much time or space). Both of them, if taught correctly, will have the health benefits of chi.
In both cases, I would say—find a teacher that is the right match for you, because how one sifu teaches can be very different from another.