I have to agree with Velo. I have a Yakima fork mount system and it is the most stable system. Sway occurs in the upright mount systems because, imo, they are unstable.
Here are the advantages, imo, of the fork mounts:
1. most stable setup- even off road.
2. security- someone is less likely to attempt theft if the front wheel is not there.
3. more aerodynamic than upright
4. you can fit more bikes/ other equipment on the rack with a fork mount.

I also have a hitch mount system:
1. much more aerodynamic
2. stable, don't even think about crosswinds or wind noise from the bikes
3.easy to use, load and unload.

Both systems have their drawbacks. If ultimate security is most important, as Nikos mentioned, than the roof fork mount would be best I think.

Personally, I like Yakima but Thule is excellent and Sportworks for a hitchmount (although mine is Yakima- just so all my parts/accessories will match).

Oh and I have never heard of any problem with stress on the fork. It is the same as if you had a wheel locked in there. I run a full carbon fork-no problems.
If anything, I would think the stress of a clamp on the frame (in a way that the frame was not designed for) as an upright mount has would cause more stress.