I would use 2X6 plates and 2X4 studs. The studs for one office will be aligned on one side of the plate and the studs for the other office will be aligned on the other side of the plate. The idea is to make the two walls independent to minimize the sound transmission. Weave the insulation between the two sets of studs.
The bigger problem you have is the 4 ft opening above the walls. You should build the walls 12 ft if you can (even 10 ft would help) or you will never isolate the sound between the two offices. --Billy