It's not so much a power thing as a tone difference. The AII is a little more like the older humbucker tone (think early Fleetwood Mac), whereas the AIV is a little more tight and sparkly, almost Fender like in the neck position. I tend to think of it as more early Free, if you listen to Paul Kossoff he has a very powerful but clean tone on a lot of the early recordings. I actually don't have a bridge AIV SM, mine is a neck with a Riff Raff bridge (which is a great combination for all sorts of music).
The PG Blues are based on an AII Stormy Monday, and they are a great set for all early rock and blues tones. Stormy Mondays will do dirt, but you will need to dig in hard to get the push from them.