Maybe I can help here.
Passives and Actives, voiced similar to each other or not, do NOT sound the same. I think overall, they are more different than similar. Doesn't matter if we are comparing Jazz/JB Vs. Mustaine Set to EMG HZ's Vs. 81/85's.
By shear virtue of the amount of gain actives have on tap, they can't sound the same. Sure, the might share some of the same qualities, but if they sounded exactly the same, why make two different products?
Actives have the potential to slam the front end of an amp in a way that passives simply cannot.
I personally don't care for actives, but thats me. SD's marketing, at least in my opinion, is on point with the Mustaine Set. They are targeting someone who wants a higher output Jazz/JB, but still wants to retain some of the tonal characteristics the passive models have.
Another comparison would be the Custom series pickups. All of them have similar output, but the difference in magnets makes a world of difference in the way they sound.
Not taking sides here bros, this is just my opinion. As a dealer, I've heard ALOT of pickups, so I'm basing my opinions on what I hear, not what I've read.