It's hard to say which is better. A good inversion table is probably more relaxing, though it doesn't allow the abdominal and posture conditioning you get with the headstand stool - or ability to twist, stretch legs etc while you're inverting.
Since the headstand stool is under $100, it's not much more to have both. If you're ankles and feet start hurting with the table you can use the stool, and if shoulders get tender with the stool, use the table. I've had both and think I've used the stool more often when I had it.