It's so long since I played a SD Jazz I would hesitate about drawing any specific comparisons but as I do own both an Emerald and Holydiver neck, I feel obliged to say something.
The Holydiver is brighter and a bit thinner than the Emerald. Given that it uses an AV magnet and 43AWG wire, the sound is surprisingly vintage. I can only put this down to the light wind, which gives the bass notes the more rounded feel I generally associate with vintage pickups. For leads, it's lovely and fluid and creamy with excellent articulation, especially in the upper register. Cleans are excellent.
Given where it is in the range, you might expect the Emerald neck to be the more vintage of the two, especially with the AIV magnet but it's not. The 43AWG wire and hot wind give it a real cut that is much more modern in style than the Holydiver. Notes are thicker and well articulated all over the neck. It doesn't have that roundness in the bass that is a feature of the Holydiver and thus comes across as more modern. For all its modern cut, the AIV magnet keeps things really sweet so in many respects it gives you the best of both worlds with the sweetness of a vintage pup but the cut of a modern one. It's a very harmonically rich pickup, which really comes across when playing cleans. Beautiful pickup.
I really like them both but for different reasons. The Emerald neck is massively popular for good reason. I think I like it because it gives me a lot of what I like about the Cold Sweat neck but with better cleans and a sweeter tone. The Holydiver was also a popular option but isn't suggested as much these days, which is a shame as it's a very musical pickup. Much underated these days I feel.