Edit: First of all, let me say

There is a TONNE of misinformation in this thread!
Simple answer this one, The Rebel Yell.
There are a few models that are similar to the JB.
Neither of these statements are correct in my opinion. If you were to listen to an
original JB, back when they were made by Seymour Duncan
the man, NOT Seymour Duncan
the company, you would notice quite a big change in the pickup over the years. The DC resistance has gone up, the output has gone up, and the tonal balance is completely different.
The BK pickup that is remarkably close to that original JB, the handmade one that Seymour himself made, is the
Holy Diver. The Holy Diver, overall, is clearer than the original JB, and it
kills the current model of the JB.
The Nailbomb could be an aggressive, nasty JB, the Crawler is a smoother and bluesier JB, the Holy Diver sounds darker than the Nailbomb and the Rebel Yell has rich mids and incredible harmonics, the sound is right between modern and vintage
Not a good comparison! Besides the Holy Diver,
none of the pickups listed are close to the JB, either the original or the new one!
Well, if you'd rather buy a BKP to a SD then you made that decision for a reason - why then ask for a BKP that sounds like an SD?
Well, maybe that's his/her only frame of reference. And your reply is just plain bitchy and trollish.
As far as I've been informed (when people have asked this question before) there is no BKP that sounds like a JB
You've been misinformed, then.
I would definitely recommend a Holy Diver as a replacement for a JB, or if you're looking to capture that original JB tone you've heard on countless albums -- a bit dry, very high output, really strong bass, tuneful growl in the lower mids, and effortless harmonics without the brightness of other pups.