I set one (by eye as it's more accurate than most or all inexpensive hardware calibrators) and then set the other based on the 1st. It works for identical monitors. Both my monitors match up perfectly.
Bridge and LR are nicer on dual monitors for sure! You can set one monitor to display catalog etc. and the other to show the 1:1 or FullScreen display. PS doesn't benefit all that much other than having more realestate to manually place image windows.
So you calibrate one display and then in /display settings/advanced settings/color management/ select the second display from the drop down and set the same default profile for the first to the second display also?