The two computers don't communicate with each other, but they can each sense both of your transmitters, using the buddy gas feature.
Hold down the middle button for >2 sec and the gas panel appears. You can see both pressures there before splashing.
In the Full display, there is a small window for buddy gas which will display continuously, and in the Standard display you can see your buddy's gas with a couple of More pushes.
Until we switched to Shearwater, my wife and I used to use a pair of Galileos and could watch each others' tanks. Good safety backup for us when one of us was distracted with photography for an extended period.