Is there a speed difference between copying files at the same time or after one another
There should be no difference. FireWire 800 operates on the physical layer, so it is all just bits of data as far as it is concerned. I recommend moving them both simultaneously, so you don't have to remember to come back and set the second one up to clone after the first is completed.

How many drives are you cloning? Personally, I recommend installing the drives from the old Mac Pro temporarily into the extra slots of the new Mac Pro and cloning them all within the new Mac Pro's box. That way you will benefit from internal SATA's 3Gb/s speeds, which are much faster than FW800.