Here's the bottom line. The views provided by an 8-inch scope are quite obviously brighter and more detailed than the views through a 6-inch scope, but a 6-incher is still definitely in the big-time, especially when used under dark skies. How different are they? There's no way to put the answer into words; you really have to see for yourself.
In my opinion, the difference is most obvious when viewing globular clusters and least obvious for the Moon and planets. Incidentally, light pollution affects the Moon and planets not at all; there's no need to travel anywhere to view them. But the massive light pollution of a major city like Salt Lake will wreak havoc on your views of nebulae and galaxies.
A good way to assess your light pollution is to step outside on a summer or early fall evening, when the bright part of the Milky Way is high in the sky. If you can't see the Milky Way immediately, you have significant light pollution. If you can't see it at all even after letting your eyes dark-adapt, you have very heavy light pollution.
As for disadvantages, they are few. An 8-incher is a bit heavier and costlier than a 6-incher, but neither should matter much unless you're right at the edge of what you can carry or afford. Most adult males can carry either one with little effort.
Collimation is distinctly more forgiving with a 6-inch f/8 than an 8-inch f/6; the likelihood of getting near-optimal views as shipped, before you collimate it at all, is much higher. But an 8-inch f/6 is still quite easy to collimate once you've learned the skill. Mostly, you're likely just to check the collimation and find that you don't need to adjust anything.