Soarin' actually barely moves at all beyond the initial lifting of the seats. It just kinda rocks back and forth a little with the movie. Any side to side motion is an illusory effect. It should have no adverse affect on an injured neck.
Star Tours certainly could. It's a bit rocky. It's not as bad as The Simpsons Ride at Universal, which is a similar kind of ride, but it will still toss you around. Plus there is no real head support, so unlike some rides where you have a headrest to steady your neck, Star Tours really doesn't have anything. I'd be careful on that one.