If the CDs (only DVDs are - or +) are finalised, then they should read on both machines. If they are DVDs then as long as they are finalised then they should work as well.
Are both machines using the same burning software, are they using 'drag and drop' as this is notorious for only being read properly on the same drive that created it.
you could always get a usb-usb file transfer cable (oh so slow)