OK, I have issues with heights, and I have balance problems, so I don't do anything that does loops, or stuff like that. I rode the DCA version of Soarin', and lived through it. I think you will have more problems with it if you don't like simulators (like back to the future) than if you don't like heights. As the movies change every few minutes, you realize that you aren't really soarin' over the Golden Gate Bridge, or an Orange tree grove, or the other things.
The only time I really didn't like it well enough was the very last scene, and there was just something about it that made me very nervous. That's all I'm sayin'.
You strap into your seat, 3 rows of 6 or 8 people. then when you "lift off", you're going around a curve toward the top, so you do see people's feet at first hanging over your head and a few feet in front of you (unless you're in the front row), but once the scenes start below you, you don't notice that at all, your attention is down toward the scenery.
All in all, the "ride" is very short, you get in place, and you come back. In between, there's swaying left and right as the movie "turns", and you get the motion of gentle movement, but nothing abrupt that I remember.