Resistance is resistance. If a cheap $0.12 pot reads 250k ohms on a meter, and the most expensive pot you can find reads the same resistance there will be absolutely zero difference in tone, or output. The sweep may be slightly different, so volume levels, or more or less high end can be bled off through the cap with both pots at the same position, but if you set them to the same resistance, even if they are at different parts of the sweep, they will sound exactly the same. This is a fact. Quality in pots comes from longer life, and consistency in how close they are to the advertised value. It has nothing at all to do with the tone.
I agree it will not directly affect the tone. I could have stated it better. With lower end instruments, the quality of the parts will not be optimum. And the 250K pot should probably be a 500K. The pots and capacitors used can give you more finite control over your tone. I have an El Cheapo Les Paul copy that now suffers from a common malady caused by low end components. When you back down the volume pot for a pickup, the tone pot loses it and becomes a volume control. This is because the capacitor is under sized. Yes, a very good pot and a very poor pot will initially read the same resistance, but over time, the better pot will maintain its readings and is less likely to become noisy.
