So, here's my trick. It has worked very well so far. Sound guys have loved the tone at FOH, I've loved it in my ears, and I have used it when working with several big-name Fractal artists as well.
YMMV, but so far, we've gotten great results.
Crank up your monitoring system, whatever that is, so you're getting good feedback, sustain, and all the nice things that come with volume.
Now, put in your ears. Turn them up to where you're pretty much just hearing them, and not the monitors in the room. This is NOT to say blow out your hearing. If you have good IEMs and they seal well, this will be a normal stage IEM volume.
Now, tweak your tone to your satisfaction in your ears. You should be using a good in-ear transmitter that has a built in, high-quality limiter, so bass frequencies won't blow out your drivers when you "chunk chunk."
Once your tone is tweaked, take out your ears. Do you like what you're hearing in your monitors/cabs? Yes? Then great. You're done. No? Then tweak a bit with your ears out. Then put them back in and go toward a middle ground. This will require only very small adjustments.
This method avoids the "Different sounds on different outputs" issue. Of course, if you like having Output 1 be FOH and Output 2 be ears, then great. But that requires a lot of EQ tweaks whenever you want to change your core tone.
(Of course, if you have a monitor guy, or you have your own board you bring to gigs, then just tweak on your system without your ears, send the tone to the board, and then tweak your ears from the board.)
If you work this method correctly, there is zero "compromise" on FOH tone, but there may perhaps be a bit of a "difference." A FOH guy is ALWAYS going to tweak your tone, anyway.