The JTV acoustic models are not great, BUT ... if you don't play hard, and let the amp do the work, I find they can work a lot better, i.e., they respond better to a lighter touch. Try that - the tendency on an actual (unamplified) acoustic is to play harder, and I find it is the reverse with a set of acoustic simulations, like on the JTV. Also, the acoustic models do not respond well to low neck position bending, or string bending in general, which is physically possible on the JTV, but not on most "real" acoustics. The solution - resist the extreme bending, and play the acoustic model as if it was the real deal with respect to bending, it will sound more natural. You wouldn't "bend" the average 12-string, why bend the JTV model? Same applies to the resonator models.
The only significant limitation of the JTV's acoustic model, IMO, is the lack of a wound 3rd string, and the string gauge "feel", due to physically smaller (electric) gauges. The simulation connot cover that "feel", so playing acoustic on the JTV doesn't feel right.
I've rigged my JTV through a Boss LS-2 (line selector pedal) with a simple loop-back, to give me volume boost when connected to a PA, and I can strum or pick softly, and still be loud enough, when I want to be. Takes a little time to play "simulated acoustic" effectively, but it is definitely do-able.
2012 Line 6 JTV-69
Plus lots of Tele's, Gretsches,
Mesa Boogie amps, Fender Blues Jr.,
... and lots of acoustic stuff