My clips are hidden on 25-year-old cassette tapes, but I hope to come across them someday...
I doubt you would hear much of it in the sound — maybe in the slight lower strings pulling that was most fun. IOW, you may not hear how special it was. I think it was also a combo of my gear, regular cabs, volume, ... — an "in the room" experience, as if the compressor was tweaked exactly for my hands and gear.
The Axe can easily do it for slamming chords and skank — the string pulling sounds remains to be seen and I will try later, as I have never tried with the updated algorithms.
OTOH, you do have to wonder why the GSP has an analog compressor? I would think it's either because they know it will be better, or because they know they are not able to write great digital code for it? Or maybe to relieve the CPU.
I don't know if analog EQ tends to be better as well. It kinda seems they chose the 3 analog sections wisely. A tube (or two) at high voltage, compressor, and EQ. I thought the thing had plenty CPU to include digital compression (although I don't know if it would take a lot CPU?), but they didn't.
Also, around Axe-Fx II, fw4 is when Cliff discovered more hints about how to add feel, IIRC. There were one or more firmwares that added an increased sense which he later removed. Maybe if that was added again as a parameter, it could help for what I experienced. Maybe that has become the Thump, etc. Too early to request. Will first see if I can get it with the new gen.