Yes. I've had trouble balancing the Jazz and the JB in the past. I've expressed several times that I don't think that combo works well. Partly because of the vastly different EQ profile,
And then the Alternative 8 is even hotter than the JB.
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The output difference between the Jazz and the JB is significant. Even with the Jazz next to the neck and JB next to bridge the output difference is noticeable, but I've never not been able to compensate for the output by adjusting their heights and still retain good tone and performance from each (I guess that's an oxymoron in regards to the JB).
I also agree that the difference in EQ makes a difference in the perceived sound level.
I don't know the mV output ratings of each pup, but if "hotter" is judged by the resistance of the pups, then the JB and the Alt8 are essentially the same...only about 2% difference which is within manufacturing tolerances. But here again the EQ and magnet differences can surely make the Alt8 sound louder than the JB.