While I could go into detail and write out a similar kind of guide for Science Powers, Foxrocks already has a great guide completed for Science Powers, so I will defer to his hard work and encourage everyone to check it out!
Am I to understand that Aux to Batteries, distributes Aux to the other 3 for 10 secs? ie if my Aux is 75, Weapons/Shields/Engines gain +25 while Aux goes down to 0 for 10 sec?
What's the downside besides no Aux based powers while this is going on?
I don't believe that the correlation is exact, it depends on your skillpoint investment and your Aux level, I believe that even with A2B 2, you don't even begin to approach a 1:1 ratio in Aux power to distribution.
You also put your Batteries into a short cooldown, for the duration of the power, which can prove costly some circumstances of battle.
Also, because your Aux goes to 0, once the power's duration has ended, the Aux power level recovers as normal (with baseline energy recovery, that's +5 power per second)