This is always a topic that gets misinterpreted along the way, so I'll try and break the systems down to give a clear understanding.
The TCMS (Train control & management system) Mitrac is effectively the same on all electrostars. It has received software updates over the years but generally this is developed on a toc by toc basis, with its requirements being adjusted to suit each customer, but the general consensus I got from a Bombardier tech was that this part of the software will talk across all styles of unit with compatible couplers however this is not formally signed off which I believe creates the 'no 375/7 coupling' rule on Southeastern.
CCTV and DOO(Driver only operation) systems differ between Electrostars. The 377's were fitted with a Faiveley DOO system, and this is only compatible with other Faiveley fitted Electrostars. CCTV even within class differs on 377's, but as there was no requirement for CCTV images to be able to be visible from the leading cab this has never been a dealbreaker (and doesn't stop a train running). 379's and 387's are fitted with a Petards DOO and CCTV system that is also fitted to the 700's. The 377/6&7's are fitted with Petards CCTV and Faiveley DOO kit.
The only system remaining that has any real impact when working in multiple is the PIS and Pass comm system. As far as I can remember the PIS just requires all units to have the same databases installed, but the Pass Comm system incompatibility is what prevents 377's and 387's coupling, but I can't see that being impossible to overcome. I don't know where the 379's fit on this area but suspect it will be 387 side of the line.
I think that covers all of the 'cross unit' systems, but it is also worth noting, that a lot of the upgrades the 377/387's are scheduled to going to create a more harmonised fleet, with (I believe) all units having the Petards CCTV. The only disappointment I can see with the GTR upgrade is that they don't move away from the Faiveley kit over to the Petards kit, which would effectively create one big fleet of Electrostars that are fully compatible with each other.
I know another area of incompatibility that was advertised was surrounding the (regulatory?) requirement for a second data backbone on the Mitrac TCMS for redundancy, and this came in at the 379 build, but when it came to the last batches of 377's it was set up so that if coupled to a compatible unit it would work, but if not it was set so it would not throw a fault and this was permitted in the relevant regulations?
TL
R 379s should be compatible with 387's at least, but compatibility has to be formally confirmed rather than theoretically so has never happened
also, quite happy to be corrected if i've got anything wrong!