I've been playing my ATK for 10 years and I've had Warwick Thumb BO and a Fender MIA Jazz.
Thumb is a great bass but it was too unique for me.
When I first got the Fender Jazz I was surprised by its clear sound. I felt like I'd been blind for all my life.
But after intensively comparing the ATK with the Jazz, my ATK now makes me feel I bought a new bass.
I used to rest my thumb only on the PU but by doing it on the neck or pickguard, I could mimick the neck PU soloed sound of the Jazz quite closely. I'm thinking about installing a neck PU though..

Low of the ATK is so special I think.
First of all, the controlable range is so wide. When I gig with the ATK, I can feel that the room is full of 'something' without sacrificing other instruments which is hard to feel with the other basses I had.
My amp has a low mid and a high mid knobs.
By boosting the low mid, I get so thick and pumping sound.
If you want more 'texture' and softer sound, diminish the low mid a bit and boost the high mid.
Well.. too much talk with my poor English.
Anyway the ATK is the only bass I'm keeping now but no regrets haha..