Here is my experience - Own all of these scattered around the house/studio.
Note 1 - I'm 53, a trademark lawyer, haven't gigged since 1993; haven't recorded a CD since 1998, but love gear:
Note. 2 - I have tin, not golden ears.
CLR - maybe just turn down the high treble or low-pass filter - Axe-FX III has the pleasure of mating with the CLR (or vice-versa)
Friedman ASM-10 - that's in my studio, so I can turn it up - sounds really great - Axe-FX II
Atomic FR - haven't used it in a while, but always sounded good using older firmware.
PowerCab - I use the Flat Setting and once in a while turn off Cabs in the AX8 (which is where my Powercab is located)
Xitone 10 inch - never loved it until I turned the tweeter off - then it sounded great. That made me think about why all patches (mine, pro, exchange) sound so grating, harsh, way too crisp not crunchy). Got rid of the FRFR high end in these and most sounded much better. Well that and Austin's patches and level setting.
Equator D5s - Monitor - I tried pretty much every 5 inch monitor and these had the least crisp high end. But I use my clear whenever possible for guitar noodling.
Your Experience may differ due to your personal likes, requirements, etc.