I’ve got a flush mount and screen that is non-flush mount (ram mount). Here are the advantages/disadvantages of a flush mount based on my experience:
Pro – its harder for people to steal, it keeps connections better, its more stable, and it looks better IMO
Con – its harder to connect and disconnect wires/plugs in the back, its a lot easier for people to steal, and sometimes the space designed for it is limited
In that photo you attached, I would personally flush mount the one on the bow but I would not flush mount the one on the console. The area for the flush mount at the console sits too low. Having to look in a downward direction while driving a boat is not exactly safe. Think of it like driving a car. You want all your instrumentation easily visible while watching straight ahead.