Does the control wiring have to be in a different conduit as the feeder conductors coming from the generator to the transfer switch if the control conductors are rated 600v
It depends on the manufacturer's instructions. Generac used to supply whips on their units that contained all of the wires, then instructed us to run separate conduits. Now they supply no whips, and we can run them all in a single conduit.
I will use whichever method suits the installation. Sometimes, like through a crawlspace, I'll use SER for the feeder and a separate 1/2" LFNC for the control wires. Other times, , like a surface run, I'l use a single PVC conduit and single wires.