A very wise man once wrote this on another forum and it has stuck with me. I have found this to be the best and most accurate explanation of diff oils:

"Keep in mind, that it is also has a lot to do with how you drive, and the design parameters for your car’s platform.

While thinner oil in the rear may make it a little unstable, “unstable” is a subjective word. In this case, “unstable” would mean that the rear end rotates quicker. Pending your driving style, this could be what you’re looking for, and could be described as “stable” to you.

I like a lot of off-power steering and the design of my car tends to push a little, so I run thin (3K) in the front.
I like a softer “punch” during acceleration, and my car’s design carries a lot of traction under acceleration, so I run 4K in the center.
My car has a shorter chassis than some of the newer revisions, so the rear of the car rotates easily and I had to actually go up to a thicker than conventional rear oil (5K) to slow down that rotation.

So, I run 3/4/5……which is somewhat abnormal. But the point is, it suits the design of the and my driving style.

As for a direct answer to your center diff question, think of it as a “punch control” or a “slipper”………….that’s the easiest way I can think of to explain it. The thicker you go in the center, the harder the “hit” from the wheels when you pull the trigger!

And no, thinner oil in the center will not apply more power to the front, it will apply less power to front AND rear. If you want the front to "pull" in the direction you have the wheels turned, go up (thicker) in the front diff. The trade-off is that it may hinder your steering while you're off the power and trying to steer through a slow turn."

Hope this helps!