In my experience, it is nearly impossible to use the Axe direct into a monitor and get the same response that you would running it into a power amp and real 12 inch guitar speakers for most applications. Certain sounds, like very clean sounds or EXTREMELY distorted sounds (big chunky death metal sort of stuff) can work well through a monitor, but any sound that falls in between, from blues and RnB to hard rock, rely upon a certain amount of feedback between the guitar and the speakers. real speakers (pushed by a real tube power section) are a certain type of eq or filter, which vibrate the air, which in turn vibrate your strings, which in turn cause upper order harmonics to pop out of the notes you are playing and (because there is feedback, either slight, over the top or somewhere in between) cause many notes and chords that you play to actually RISE in volume and harmonic content after the initial attack as opposed to falling off, or perhaps staying the same.
So, you can get very close to the sound of speakers with cab sims, but once that sound is pumped back at your guitar with a full range monitor (and not a real guitar cab with a 12 run by a pushed power amp) you will find that you are going to get COMPLETELY different feedback characteristics, most of which are actually unpleasant sounding, and which will not positively impact the sounds you are making. In other words, the critical element of air vibrating your strings and causing upper order harmonics and feedback has been removed. That is the sound you are hearing and mo model can recreate it.
that being said, use the axe with real speakers, a real pushed power amp (your 20 20 is probably perfect as long as it provides you enough head room) and, use no cab sims and experiment with where to put the power amp settings like sag, and you will find that you suddenly have that critical element back, but with the massive array of fx and amp models that the Axefx has to offer.
For that matter ( I am going to start to experiment with this myself) having an FRFR powered monitor (it must be coaxial. Period. don't even THINK of using anything else) ALONG with a real amp or tube power amo and speakers and running it both as a wet dry setup or even as its own source for certain sounds that sound better in that setting (again, certain very clean sounds and VERY chunky distortion sounds) would give you the entire experience.
So, in short, a powered monitor will NEVER (regardless of which cab sim or eq setting you use) cause the type of feedback that a guitar cab (run by a pushed tube power) would, and without it, you will never achieve really great tone. You can get close, but it will always seem dead and lacking the voice like element. I would love to be proven wrong, but so far, no one has come up with a FRFR solution for controlled feedback ala Hendrix, Robben Ford, Eric Clapton, Duane Allman, Eric Johnson, Joe Bonamassa, and countless other great plays whose tones absolutely depend on it.
