Q2 are based on the same common principal.
The Q2 diff is designed and made by Torsen, and the Quaife ATB diff by Quaife, but they are direct competitors and could in theory have different setups (torque bias ratio etc).
From my driving of both on a GTA I personally couldn't tell much difference, and if the Q2 is still 200 quid or so cheaper than the Quaife I would certainly recommend that. I dont actually know if the Quaife is any better in fact. At Mondello, If anything, I would have to say that while the number of laps were limited I suffered more inside wheelspin with a quaife than with a Q2, but at the Ring in another GTA (PeterK's) the Quaife (from Madeno Racing) felt perfect.
I am putting this down to the higher ride height of the car that suffered more wheelspin so its not really a direct comparison with identical cars, but my temptation is to give the Q2 the edge for a GTA.
I have driven a lot with the Q2 on my supercharged GTA, and it performed very well, and took way way more power than it was designed to reliably.
I also used a quaife on 2 standardish GTAs for several laps track use (at Mondello, and the Ring), they felt pretty much identical to the Q2, but I didn't get to test the Quaife on pure road use - I'm sure its the same as the Q2 in that regard - both a bit squirmey on uneven surfaces..
Coincidentally I have recently had a Quaife diff fitted to my (shared with 2 others) Autotest starlet, and wow that made an enormous difference for very tight turns (..Mind you thats something the GTA cant do!)
Heres a clip, of our instructor driving our Autotest car, in VERY slippy conditions, and our Autotest tyres aren't meant to be very grippy but the traction off the line and around corners as amazingly improved.
Without the Quaife diff, wheelspin would be very very hard to control in those conditions..
Autotest Practice Mondello 14th Dec 208 Rocket Ron- Video