You're on the right track, I think.
Both tornados and hurricanes exhibit vorticity and wind(a vector quantity). The big difference is the scale, but at a given point the wind velocity is what it is in both cases. Now consider the vorticity and lift. Much of the extreme damage we see in a tornado results from the(straight line) wind at a point PLUS the very strong localized lift within the more localized vorticity- an intense localized suction vortex. This produces the forces we see in videos that dramatically rips off roofs and uproots trees while lifting the debris rapidly upwards. Tornados are more intense, or 'violent' in a much more localized area.