Usually there is no difference. There's just a pickup and output jack on the acoustic so you can plug it into an amp.
If done well, the difference should be negligible but a lot of times on lower end instruments pickup installations will dampen tone to some degree. You have to think about the fact that you're cutting wood out of the guitar and replacing it with electronics. Sometimes there'll be less resonance and volume and an overall more muted tone That being said, I played a Martin OMC and an OMC no E side by side and couldn't have told you the difference if blind folded.
Winner of the 2011 Virginia Guitar Festival

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While it is true, (as was mentioned), that the preamp takes away internal volume and resonance from an identical fully acoustic instrument, that's not really the primary consideration or cause for sound difference.

A cutaway, (if present), and the material used in construction, have more profound effects on the sound.

Even with all that said, personally I'd opt for an A-E guitar every time.

Acoustic electrics are made to be plugged in, and they generally sound better that way.

It's much more aggravation and expense to retrofit and acoustic guitar with electronics, should you change your mind after you've bought an acoustic only guitar.

I think people change their mind about electronics more often than not. Even mid-price A-Es are often equipped with XLR connectors for DI into the PA or mixing board.

Amplifiers provide more than just volume increase. The delay and reverb which are usually available, create ambiance for you, even in dull rooms.