Shelving and how it works is a really important consideration when setting your sound. You explained it well.
But if you are looking for better EQ control, parametric controls are far superior to shelving types. You can target individual frequencies to cut or boost instead of cutting or boosting a range of frequencies. This is the reason, and for my money, the best reason to consider the new Mesa D-800 when buying a new amp. It’s also why I love my Eden rigs where it will be a cold day in h*ll when I give them up.
The shelving type EQ contributes to that “baked in sound” often discussed here that either you like it or not. I had an Acoustic 370, and a SWR Workingman that had certain annoying frequencies you couldn’t get rid of that drove me to distraction.
Usually the Bass and Treble controls on amps are shelving and mid band controls are peaking. Pretty sure this is how all of the Mesa Subway amps are setup.
Parametric is peaking, but you can control the frequency centers, and with full parametric you can also control the band width. The D800 has fixed frequencies on all tone controls. The D800+ and WD800 have semi-parametric midrange controls. These are semi-parametric because the bandwidth is fixed. If I were in the market for a new amp, these two would be at the top of my list and I think I would probably go with the WD800 for its expanded tone control capabilities.
IMHO the GBE1200 does not have much of a baked in tone. In my experience a baked in tone is often associated with an amp that cannot be dialed in flat, and this amp is pretty neutral if you want it to be. I believe @agedhorse uses the term "lightly voiced."
I think he did a great job in selecting the bandwidth and frequency centers of the tone controls. But of course each player has different tastes, so not everyone loves this fabulous amp. I responds really well to EQ inputs, so you can get a lot of sounds out of it by blending the two channels and experimenting with different gain and EQ settings, but some players don't enjoy tweaking regardless of how easy the amp is to dial in.