The computer type itself should not matter as the RS422 port is on the breakout cable of the card. So it should be governed by the card and the driver not the computer.
Are you suggesting that the same decklink card works in a different system?
Does your patch panel handle the crossover for the RS422 cable? I think if you patch two RS422 cables together they will both crossover and uncross themselves. On our routers it is handled for you, so all you need are two patch cables, one to the card and one to the deck. But you mentioned a patch panel. I'm wondering if you are ending with a straight though connection which would effectively connect the Tx to Tx and Rx to Rx.