To maximize DPS with deflector/engine/shields, we normally use the Undine deflector with either the Romulan engines and resilient Fleet shields, or the Undine deflector with the Nukara shield and engines.

If we ignore the shields (assuming you have good survivability), the difference is 26.2 Starship Attack Pattern vs 2.5% Weapon Damage Bonus.

If you're a Tactical captain, the former tends to be the obvious choice as it will boost APA, APO, and APB, all of which you likely carry. (Is that right? Or is it not such an obvious choice? Not a Tac, so I don't know.) What about for the rest of us without APA?

The wiki here claims the 2.5% boost to weapon damage was negligible, but research shows that it's a 2.5% bonus (like the Obelisk 10% AP), not strength (like [ Pla] or Tactical consoles). As such, it increases our DPS by an actual 2.5%.

I plotted the data from the skill effects table and linearly extrapolated how Starship Attack Patterns affect the resistance debuff and damage bonus of APB3 and APO3 respectively. Excel gave me 0.1709x 32.939 for APB3, and 0.084x 16.76 for APO3.

At a skill of 99, APO gives a 25% damage bonus. At a skill of 125.2, APO gives a 27.2778% damage bonus. This means the Romulan engine gives 2.3% damage bonus with APO3, but APO3 is only active at most 1/3rd of the time - so the Nukara set's constant 2.5% bonus results in higher DPS.

At a skill of 99, APB3 gives a -50% damage resistance debuff. At a skill of 125.2, APB3 gives a -54.33468% damage resistance debuff. So the Romulan engines give an extra 4.3% DRR debuff with APB3, and it's possible (with 3 appropriate DOffs) to have almost 100% uptime with APB3. Damage resistance debuffing appears to have some weird formulas that make my brain try to run away, but since it only applies to Hull anyway, I'm not sure if the slight increase is equal or greater to a 2.5% damage bonus.

Given the above, it seems to me that (APA aside, and assuming the Undine deflector), the Nukara set should give higher DPS than the Romulan engine with Fleet shields.

Can anyone confirm or refute this?

Update (20140720):

I parsed the three combinations in SB234, since ISE ended up with too many variables (very high Standard Deviation values and percentages).

Deflector   Engines     Shield      Mean         StDev      StDev%
CoCo        Nuka        Nuka        7,472.10     285.14     3.82%
CoCo        Romu        Nuka        7,800.44     299.35     3.84%
Nuka        Romu        Nuka        7,169.71     288.42     4.02%

So it looks like the CC/Rom/Fleet Shield thing is indeed the best. Conformity!