I've got two "Hollywood" kits, one with the disappearing spurs (1968) and one with the gull-wings (1966). The disappearing spurs (only 1 pair of them, not two) definitely hold the bass drum more stable (less rocking movement left to right) and less "walking away" from the drummer.
From this limited experience, I wonder why Ludwig changed from the disappearing spurs to gull wings. And I wonder if other drummers have had this same experience. I would think that TWO pairs of disappearing spurs - like Jaghog has now - would be a super stable platform.
Regards, mb