Mike
I'm not sure it's entirely a numbers game. In recent years I've taken a strong liking to nine hole courses over here in Scotland and have actively sought them out. A lot of these nine holers play over scrap bits of land and consequently the design tends to be quirky and unconventional which has great appeal for me. They also tend to be in relatively remote locations with basic facilities and tend to be quite rustic in character which also adds to the appeal, for me at least. You don't tend to get all that with 18 holers.
With your example, I expect there would be a constant queue to play the 6 hole course which might just push me towards the 18 hole course, irrespective of the difference in quality.
Niall