Someone mentioned light gathering power. While a 12" might have 4 times that of a 6", it's only half the story, in more ways than one. What matters is what you can actually do with all that extra light, and it's less than the number might suggest.
It takes 4 times more light to show an image
twice as big, at the same brightness.
A factor of 2, not 4 
. The 120ED vs Lightbridge simulation, although not exactly 2 times bigger, shows that nicely.
Similarly, resolving power (whether based Dawes or Rayleigh) is proportionate to the lens or mirror diameter. The diameter is the denominator in the equations. According to them, a 12" will resolve
twice "as finely" as 6".
A factor of 2, not 4 .
The answer to me is surprisingly simple. A 12" is,
at most twice as good as a 6", not 4 times as the "light gathering power" thingy may suggest, provided both scopes of comparable quality. A 6" achro vs. a 12" Zambuto equipped whatever will give a vastly different outcome. Similarly, if the 6" was a high grade APO, and the 12" anything less than a top-notch newt, I would not be surprised if that margin became desperately thin.
I stand to be corrected though.