Mart,
John is absolutely correct, the hovering task in a vectored thrust is relatively simple one as compared to a helicopter, mostly because the nasty cross couplings and rotor responses to changes in velocity and direction (the bulk of the problem we face) are simply not there.
OTOH, the concept of hovering and the need to control acceleration/attitude while making a double integration to achieve position is still there, so that some training is necessary, but the Harrier "feels" like it has SAS even when unaugmented.
The XF-35 has a great deal of augmentation so that it is a position=hold control while hovering. Look at the videos of it hovering to see the rapid, automatic nozzel movements commanded by its stability systems. see the clip "X-35B Landing" on this page and look closely at how hard the rear nozzel is working:
http://www.jsf.mil/gallery/gal_video.htm