You get a more hollow midrange-y sound with the cap engaged. Like using just the neck pup with a little extra snap to it.
I generally prefer the standard 'modern' tone, but for some songs I like to pull the pot, and back off both tones to get more of an upright-ish sound depending on where I pluck.
It's just a little added versatility.
The modern tone is a very throaty growl with everything full on, not the same as a 4001 at all. the pups are wound hotter, the pots are different values, and the construction is subtly different, but you could probably come close to a 4001 tone by changing the pups and pots.
I'm very glad I bought mine, and I think the push/pull pot is a good idea, and well worth adding to older basses.
It's not something I'd use all of the time, but it's nice to have the option to use it whenever you want.