The question in your title, and the question in your post are slightly different. I'll try to tackle both.
(Oops . . . no they aren't.) :laugh2:
Relative to a volume control, the resistance affects the "load" that the pickup "sees". Its how much work, you're asking the little AC generator to do. The "tone" the pickup provides is related to how hard you're making it sweat. Lower pot value, (250 vs 500), is a greater load. It works harder and doesn't hit the high notes as well. Or, you might say its smoother, like a heavier flywheel.
Relative to a tone control is different. A 250k and a 500k is exactly the same . . . except that the 250 is "preset" halfway down. (Electrically, not physically.) You can roll a 500k tone control down to 250. You can't roll a 250 "up" to 500. If you don't need the extra high-end, a 250 gives a bit more rotational resolution.