So I've had modeling stuff for years, and always spent time fiddling around to get a good sound anytime anything changed. Finally I moved to this:
guitar -> pedals -> modeler -> EQ pedal -> amp -> speakers
I've tuned my patches to sound good over headphones using the headphone out. Then I tweak the EQ pedal so that I get the same/similar sound from the amp.
Now whenever I plug into a new amp, I can just adjust the EQ pedal to match the headphones and away I go. I generally start with a high-gain patch because it tends to saturate all the frequencies and makes it easier.
I keep a list of EQ pedal settings for each amp so that I can remember where it was set for that amp. I'm currently running a Pod xtLive into a Fender Mustang IV (2x12 stereo combo). But I can move to other amps and get "approximately" the same tones.
Once I started doing this, I'd try old patches and I realized that I was tweaking all kinds of settings---pedal eq, amp eq, global eq---in order to compensate for the amp's basic lack of flatness. Pushing that problem to right before the input to the amp makes everything way more consistent. This approach reduces the character that the amp contributes to the whole sound, but in this case that's what I want.