Its just various ways to skin the cat.
The cat being high gain, detuned metal. The requirements being tightness and clarity and the problem being, all things being equal, if you just crank up the number of turns on a wind and do nothing else you will lose top end and clarity.
There are various solutions. EMGs, for example (and this explains your confusion at the use of 85s, 707s and 808s) are very weak winds with very weak magnets that give an *extremely* clear and tight signal off the wind, but its very weak and very bright, so a preamp is used to bring it up to level and shape it somewhat (mainly bring up the low end) before sending to the amp.
BKs use scatterwinding, coil offsets and quite low power winds with very powerfull magnet/s in variying combinations to aim for the same effect.
Another way that many settle on is to use a weaker pickup altogether and rely on the masses of gain and compression available in modern amps and amp sims (like the axe fx nolly uses), acting on the clearer signal from the guitar to bring it into metal territory.
No way is wrong. Some ways work better with some signal chains than others, in my experience. Running a low output pickup into a high gain amp, for example, I've always found to lack the percussive effect in the low end, and wrestled with highs being too shrill. Works better into modellers, where the models are doing more aggresive toneshaping, stamping their sound on it more, but acting on the clearer signal. On the other hand, actives into a singal chain thats quite 'processed' or has a lot of diode clipping can lead to sterility-death of you sound and thin, weak tone, whereas using them as god intended (i.e. as they were designed to do; hammering the hell out of a valve pre) can yield superb results. To my ears the BK high output answers are somewhere in between and work with most things at least quite well.
The emerald is an often overlooked pickup. I've never played one, or even heard one for that matter. It may work very well, cant say. Spec wise it should be able to metal out, if you have an appropriate signal chain, but I couldnt say for sure.
P.S. Not listening to avril lavigne. Not unless theres some sort of compensation for mental trauma suffered :P