"Thinness" or "thickness" of your sound has more to do with your pickups than with your pots. The pots will contribute to the overall tonal quality of the guitar, but the tone originates with the pickups. With pickups, the number of wraps of wire around the magnets really is the contributing factor to "thickness" vs. "thinness". Fewer wraps = clear, bell-like tone & lower output. More wraps = more middle, more "muddy" tone & higher output.
You can think of this like plumbing and water. 250K would be a narrow pipe and 500K would be a bigger pipe. It wouldn't matter if you put in a bigger pipe if you only have a trickle of water coming through to start with. So pickups with fewer wraps would give you a trickle or a stream, and pickups with more wraps would give you more of a river.
In my experience, it's more common to replace pickups than to change pots. The LIndy Fralin and Seymour Duncan sites are really good starting pionts for reading up on the differences in tone and output for pickups.