I'm one who can feel the difference between 1-11/16" and 1-3/4" most of the time and prefer the wider one for my 75% finger picked / 25% strummed use. On a Taylor neck either nut width works for me, hence my 114ce and my former T5 classic. But on a Martin neck I just cannot make it work. I can play any Taylor neck for literally hours without any pain, but a 1-11/16" Martin MLO neck and my fretting hand kills me after 20 minutes and aches the rest of the day. I have to be really careful when someone asks me to demo their Martin. A few minutes and my left hand is done for the whole day. That forced me to sell off the Martin guitars that we once owned (J-40, D-28, 000-16).
As for 1-23/32" on the GT versus 1-3/4" on others, I could not feel the difference in nut width on the GT during a brief test play in a store, but I have not spent real time with one. The Urban Ash version was underwhelming to my ears.
The GT's have a different neck carve (I think) as do the GP's. Hand feel is a complex combination of nut width, fret board radius, action, neck carve, rolled edges, fret height, and sunspots. [OK maybe not the last one]. Given the dollar difference, the A12 prevails handily over the GT, and the arm bevel is a nice bonus. I don't get hung up on laminated versus solid body woods anyway. As long as the guitar top is solid wood -- and they are on ALL Taylor guitars -- then I'm good. A12 for the win!