I've done a couple test rides on older Shimano Di2 and eTap. I could not tell a difference. I know eTap is slower, but I think we are talking fractions of seconds difference.

As for the separate batteries, the FD battery should die a lot slower than the RD battery. Sram's argument is that if the RD battery dies, just put the FD on the chainring you want, then swap the FD and RD batteries so the RD will still be good to go.