The Classics are nothing like the Moderns, though. Like, really, at all.
I'm a big fan of the 81 as well. But I also like the Moderns. But the Classics are way different. They sound NOTHING like Moderns or EMG's. You see how the Modern Ceramic is sorta like an more polite 81? I agree. But te Classics are nothing like that at all. They're very passive-sounding and feeling, just with the Fishman clarity and consistency. Give them a try. Worst case scenario, you can move them. They're so hyped right now, I doubt you'd have any trouble or lose too much.
I am a big Fishman fan. But I do agree that there's a lot of hype around them like they're the be-all-end-all of pickups, and they're not. I like them, but I still keep my passives around.
Another one you'd maybe like is the EMG 57, but you've probably already tried it? But that one is way closer to the 81 than to the JB.