Interesting. My guitar is a nylon string, and there is a significant difference between "acoustic" amps voiced for steel string guitar and nylon string guitar as opposed to FRFR amps. In my experience, of course. I haven't tried in the Aux In, since the regular guitar input worked so well for me (if it ain't broke, don't fix it)...
The sound is ultimately a number of factors - the guitar pickup/preamp, the effects box, and (especially) the speakers, where "FRFR" really came into being only within the past five years or so. (The first speaker that really worked for me was the Fishman SA-220).
If you already have an excellent guitar it may not make a difference - but nylon string guitars have different voicing than steel string, not to mention electric - and not to mention Flamenco....