I haven't used it live but I recorded through the Axe-FX with acoustic a lot and there are a few nice tone sweetening tools:
Compression: There are a couple of ways to use compression; to even out the tone and as more of an effect that brings the sound forward. I usually use some subtle compression first in the chain just to tame any peaks in the playing and another nearer the end (before any reverb/delay though) to give it some more body and make it sit more upfront.
Parallel compression is nice for the later one. Set it up more aggressively with a lower threshold and higher ratio but blend the dry signal back in with the mix control. If you're feeling particularly experimental you can run two or more compressors in parallel with different settings and blend them and the dry to taste with the mixer block.
Drive: A little Tape Distortion can be a nice effect on an acoustic. The Mix knob is helpful here as well - sometimes a heavier distortion mixed low works better than a more subtle distortion 100% wet.
Amp Block: The Tube Pre adds some nice distortion and can be a handy tone shaper.
Cab Block: IR #F.02 1024 Totally Flat is the same as bypassing the IR part of the Cab Block but allows you to use the other tools in there. The preamps add some nice colour and saturation if you want it. Transformer, Tube, FET and Vintage are all nice on acoustic.
PEQ: As mentioned above PEQ is a useful tone shaper and for controlling feedback. Particularly handy when you're playing with others and you need to carve out some space for the other players/vocals.
Tonematch: Many people have matched the piezo of their guitar to a miced tone with great results. If you have a good mic and a decent room this is highly recommended.
Reverb: Pretty obvious.
Delay: A lot of engineers use a short delay with low feedback in place of reverb to give a sense of space but without getting clutter. A short Stereo Delay can also be a nice way to stereoise your sound, but I probably wouldn't use it in your case because there's already a second guitar.
Enhancer: Some people like a little enhancer on acoustic. I don't - sounds too processed/80s to me - but worth experimenting to see what you like and what fits the situation.
To be clear I wouldn't suggest using all of the above at the same time, especially the ones that introduce saturation, but judicious amounts of selected ones can give the sound that studio finish
