I have two ATK 805 from before June 2013, one ATK 805 from June 2013, and two ATK 305 from the 90s and I've tried a few others in store. The 90s ATK305s have a nice chunky neck. My two ATK805 made before june 2013 have a nice chunky neck. The one made in June 2013 has a little slimmer neck but still nicely rounded, not that shallow feeling Fender modern C stuff.
The other ATK 5 strings I have tried have flatter, thinner, feeling necks.
I don't know how well my 5 string ATK experience transfers to 4 string ATK basses because I never played a 4 string ATK. Ibanez is not exactly consistent all the time either. For example, I've tried their TMB-100 and TMB-105 basses but the TMB-100 has a nice chunky neck and the 5 string has a wide flat feeling neck.
There is no substitute for trying them yourself.