I used to use my standard back in the days with a mesa boogie 50/50 and 4x12 cab. The sound was excellent, albeit similar from patch to patch (especially for hi-gain sounds) since every amp model was going through the same PA and cab. I then sold the 50/50 and used an art sla2. The sound was even better (less coloring from the PA) but still similar from patch to patch (again because of the use of the same 4x12 cab).
I had always used the axe in this configuration with cab sims off and power amp sim on.
Then I got rid of the 4x12 cab and bought a pair of studio monitors. Now (and with the axe 2) I can hear every little thing when I'm trying to adjust anything and every amp and cab/mic combination is vastly different from one another.
I would say that your problem lies somewhere in your setup (maybe sth wrong with the cables, Ohm matching, levels, possibly phase problems from stereo to mono etc). Start with an empty patch with just an amp, make sure everything is connected correctly and go through your I/O menu (all pages) to see that everything is as it should be (e.g. correct input calibration, mono output selection etc).
It SHOULD be REALLY easy to get an awesome sound (if everything is connected correctly), without any "excessive" tweaking, just as if you were to tweak a real amp. If this doesn't happen, then there is something wrong with either the rest of the hardware (since you say that through headphones it sounds fine), or with something else in your signal chain (e.g. bad cables, guitar with active pickups and low battery etc).