I'm not sure if cockpit displays are swapped between the pilot and copilot. Usually, the pilot (or for that matter copilot) will have their PFD (Primary Flight Display) right in from of them, with the navigation (and other) displays on their side. My guess is that this is the reason the displays appear symmetric.

[![Cockpit display][1]][1]

Source: www.avweb.com

This photo, though from a helicopter (Bell 412) clearly shows the pilot and copilot PFDs right in front of them, in the same line as cyclic and between the rudder pedals. 

[![Bell 412 cockpit][2]][2]

Source: latinairforces.blogspot.com

Also, note that the information displayed could be switched between the two displays. Usually one display always shows the important flight info (i.e. acts as the PFD) while the other can be changed to show what the pilot wants.


  [1]: https://i.sstatic.net/xg9id.gif
  [2]: https://i.sstatic.net/hUrfM.jpg