I think there's a subtle difference between the amplification produced by an active transducer and by an all-electric pickup. I have an i-Beam fitted to a Martin XC1T. It sounds very nice but quite different from the 1960s DeArmond pickup on my Chisholm hollow-body. The DeArmond - fitted across the sound hole - is outputting the sound of the amplified strings, whereas the iBeam - fitted under the bridge - is outputting more of the overall acoustic sound of the guitar.

I suspect that, were I to reverse the fittings, the hollow-body would probably sound quite thin and weedy; the DeArmond would make both guitars sound more or less the same.

Just a guess, of course, because I've never tried the experiment.