Darthphineas may have something to add to my comment since he's been so helpful on my threads in the past.
Of Duncan passive high gains, I've tried the JB, DD, Alt 8, and Full Shred. Most of my guitars are alder/maple/rosewood bolt ons--mid priced Japanese models. Licensed Floyds.
IMO, the main distinction among all of them is the amount of saturation you get, as well as slightly different EQ curves.
First, make sure your pickup matches your guitar and amp. If you have a high gain amp, try a lower output pickup so you have more clarity. Way too many metal bands now run a high output pickup through a high gain amp and their tone sounds like a nest of chainsaws or flub-a-flub scooped Recto. If you have a lower gain amp, a higher output pickup will offset that.
I prefer boosting the front end of my amp slightly as opposed to using a hot pickup since I can dial in or remove saturation at will. You're stuck with whatever a pickup gives. Lower output pickups have more clarity and dynamics generally, and it's very difficult to clean up a hot pickup. I dialed in a good metal sound with Gibson 57 Classics once, but I've had less success cleaning up a Distortion.
Second, in my experience, the JB is a hugely overrated pickup because it is loose in the bass and low mids. It is a fine pickup for chunky hard rock rhythm at moderate tempo, but when the speed gets faster it gets loose. It sounds fine in a mix but by itself it is butt ugly. You can work with it, but prepare to use a high pass filter to roll off some of that low end. The low mids and upper mid honk will need work depending upon your taste. I suspect the JB got its reputation because it is a good all rounder for rock and, back in the pre Internet days, it was easier to make a JB work than to compare so many types of pickups.
The DD has tighter bass, more saturation, and more high end cut than the JB, but it can be harsh. I'd start there. I haven't tried an Invader, but it sounds like its bass, mids, and saturation would overwhelm most guitars. The Alternative 8 is similar to a DD but with more bass and slightly less cutting highs.
Think about the difference in the JB and DD as being like a Marshall vs. a 5150. The Marshall has classic tone but the 5150 is more saturated and, some would say, harsh. But the DD suits extreme metal better than the JB does.
So far, my favorite set is the Full Shred. They're the most tonally neutral of the ones I have tried. Some people say they're bland, but I find them balanced. I haven't tried the BWs, but the Shreds are great for moderate rock all the way to death metal if you tweak your signal chain. I've seen several guys here say the Full Shred is fine for drop tuning because it has a really punchy, defined sound.
JB, DD, Alt 8, and Full Shreds will all give you great harmonics, but IMO the Full Shred has the most touch and sensitivity--ideal for articulate solos and those clean to distorted changes in metalcore.
Something you may want to think about is trying full sets first as opposed to individual pups in order to find a good neck pup. Normally the full sets work well. I'm used to an EMG 60, so even the Duncan Jazz is a bit warm to me.
Ultimately, I think the DD set is what you want. That said, I'm not sold on the Distortion neck pup. I've never tried it, but my experience with high gain ceramic pups in the neck is not good. If you want a bright clean sound in the neck like a lot of metal guys use (brighter than a Jazz), you may have trouble finding a Duncan that will do it.
Maybe one of the more experienced guys can help with a bright neck pup.