Okay, I got to try out the Enterprise-D, and have a few observations:
First of all, graphically the new "Operations" is essentially Artemis's Engineering system grid display, only simplified. There is a cutaway of the Enterprise-D (an MSD, in Star Trek terms) and you direct crew members to systems. (And you can see the crewmen moving around on the ship, and even select them to monitor their progress) So in effect, Star Trek: Bridge Crew improved the Engineering interface by bringing it closer to Artemis. 😃 Or possibly FTL...
In practice, however, the new display is interesting. It takes the place of the Aegis's systems rerouting, as I guessed, and instead the systems that you send crew to get a boost. You have 2 crewmen of each division (Engineering, Command and Science) and about 3-4 systems per division to send them to. Or 6 crew across 10 systems. Obviously, crew from the same division do better at a system, and you can assign up to 3 to each, for increased enhancement of that system. Of course, that takes manpower away from other systems.
In addition to the standard three systems that you can boost with routing, there are systems that you can boost to give the Enterprise-D a special advantage. For example, the shield modulation I mentioned before is accomplished by sending a crewman to Shield Control, which will both boost shield strength and enable shield modulation. Tactical can use this feature to make the shields more robust against the current target.
The systems and their bonuses are: (in no particular order, but divided by division)
Shields - Boosts shield strength and enables shield modulation
Phasers - Boosts phaser fire rate and enables precision targeting
Torpedoes - Boosts torpedo load rate
Engineering - Boosts engine power
Thruster Control - Boosts local movement speed
Transporter Room - Reduces time to get transporter lock
Scanners - Reduces scan time
Computer - Provides immunity to anomaly effects (Operations has a panel to activate this)
Astrophysics - Allows sensors to penetrate cloak (ditto)
Sickbay - Crewmen can get injured, send them here to heal them
Crewman health is represented by a heart, which is somehow hilarious to me, seeing the little hearts all over the ship system display. 😃 I may have had Computer and Astrophysics backwards, but the new features all allow the Enterprise-D to get around the various annoyances and hazards that are serious to the other two ships. Of course, Klingons could always cloak but with Romulans in the game now the ability to see through the cloak gives the Enterprise-D a definite advantage.
I'm still not sure about precision fire. It appears to still be possible to target subsystems, but unlike the Aegis there is only one fire mode, Burst. It is possible that the precision shot (which as noted requires a crewman in Phaser Control) works like Subsystem Targeting, but you have to fire at the moment an arrow crosses a target. I'll have to test the system to see how it works.
I'll also have to double check if the original Enterprise has crew commands for Subsystem Targeting. Presumably the commands wouldn't be there if the interface didn't let you. I'll also note that in a previous update they changed the bridge officer interface so instead of looking at the station you wanted to control, there is instead three buttons at the bottom to command Helm, Tactical and Engineering. I wasn't sure why that was needed, but now I realize it's because if you're sitting in the Captain's chair on the Enterprise-D, you have to turn around and look behind you to access Tactical. They must have decided looking at the station was too difficult.
A previous addition added IBM's Watson as a voice recognition system, so the physical interface is actually a little redundant now. Although I still use it.
Finally, I will add two things that totally blew me away. First, when you start the game, it plays the Star Trek: TNG intro, without the voiceover or sound effects, but with the game's theme song instead. Still, in VR the experience of actually being INSIDE the intro and experiencing it going on around you instead of watching it from outside is unbelievable. And in the "attract mode" or while you are waiting to start the game, instead of flying around the Aegis in a shuttle as before, you are now flying around the Enterprise-D. You can see the Aegis in the background on another arm of the spacedock, and the original Enterprise is also nearby in the other direction. I don't even remember if the original Enterprise could be seen on this screen before.
In both cases, the technical limitations of the PS4 do kind of detract from the experience. It might be better on the PC, I don't know. The texture on the Enterprise-D is kind of flat, and in the intro, the first constellation you fly into just looks off. But even with all the flaws, it's an experience you have to see in VR. I literally sat for ten or twenty minutes just circling around the Enterprise-D and taking it all in.