Back when I raced touring cars, I was always tearing into the diffs to tune the car for different tracks. A lot of it comes down to driver style, track layout, and how you want the car to feel also. Thicker oil in the front diff will help "pull" the car through the corner and make it less tail happy, but at the expense of wanting to push the front more. The inverse will give you more aggressive turn in, and the ability to "push" the car into and through the corner with throttle, but you need a good feel for your braking and throttle inputs, as the car will want to rotate the rear more. Bear in mind, spring rates, shock pistons and oil weight, camber, caster, and roll center all play a part in this as well. I generally ran thicker rear diff fluid on large fast tracks where I could use the throttle to help plant the rear, and the inverse on tight twisty layouts where coming off the corner was more important, as you couldn't carry momentum like a big track. Tire wear patterns will help tell you what the car is doing also. If the fronts are wearing faster than the rear, you're over driving the front end. If the rears are wearing much faster than the fronts, the car is either lighting up the rears from too much diff (you'll realize that one pretty quickly

), or your suspension setup is off and not letting weight transfer quick enough under throttle. Which will still spin the tires, but you if your suspension setup is on you won't have near as much violent snap oversteer.
When I first went from 2wd stadium trucks to touring cars, I felt like you needed an engineering degree to get the darn things to handle properly.