My understanding from the Bettershifting site, is that with the older two button ones, you can configure to shift up and down as you like (as I have them configured) the left pair of buttons controlling the front mech, the right pair controlling the rear mech.
However the single button ones, when used 2x, can only operate in synchronised mode, that is they choose to change the big ring, depending on where you are on the cassette. Though I believe it is programmable using the shimano software.
I have the two button (older) Di2 with bar end and brake lever shifters. The problem I had installing them with bars ends close together is that the buttons are designed to be on the inside - so if the bars ends have an entry point for the Di2 cable underneath (as aerocoach and D2Z bars do) , the switches are very close together and hard to get thumbs in as well to get to the buttons. I ended up taking a small drill to the Di2 shifters to carve out a short slot that enabled me to change the exit point of the Di2 cable position to further around the switch. I can now position the shifter and buttons at an angle more facing me, allowing the cable to exit at 60+ degrees from where it normally exited… and a much better position for my thumbs and hands close together. I still occasionally accidentally shift the big one, but its not an issue.
Shimamo did not introduce new Di2 shifters for 12 speed, so there is a software upgrade to the Di2 (as well as having to but the new front & real mech and batteries), that makes upgrades from 11 to 12 speed relatively simple. This is a useful read on both synchronised shifting, choice of set-up and 11-12 speed conversion.