I was sort of hoping you were using RGB SCART as that, depending on the TV/Settings, can produce what is called SCART shift. It is a sync issue which I think is caused by a slight delay in processing the RGB signal so the horizontal positioning of the picture area shifts, usually, right, leaving a black border on the left.
On CRTs this was often hidden behind the front bezels and/or by the TV's overscan. Some higher end TVs, like my Sony WS Wega, had manual menu enabled RGB correction and others seemed to correct it autuomatically.
Anyway RGB SCART shift is obviously not the case here. So if it is not an in-game screen positioning issue I really can't think why this is only occurring with these particular games.
There can be some weirdness with progressive scan resolution support in some games of both PAL and NTSC origin although that usually just means they don't display. The later Xbox version video encoder may also cause issues with certain games.
However I do recall at least one other (GTA3 I think) where simply turning off the widescreen option resolved some progressive scan display problem although not what you've described. Worth a try though.