Technically CT doesn't give you any advantage. In practice it makes a difference in how YOU handle the plane. In some particular planes (P38, mossie) CT can put you in trouble.
What you have to realize is that CT constantly adjusts your trim to a theoretical level flight at your given speed. If you are in a turn fight and loose speed the CT will continue to trim nose-up thus causing the same effect as you pulling harder on the stick - even though you hold it still. I find it makes me blow away more energy than I want to.
If you stall out the plane, due to the loss of speed, CT will trim you full-up making it harder to regain control, especially if you start to spin. In the Mosquito, due to what appears to be a bug in center of gravity, it is almost impossible you get out of a spin or deep stall when the CT is on - you just can't get the nose down and gain forward speed.
The other problem is high speed dive. CT will continually trim you nose-down making it harder to pull out of the dive.
Some people leave it on and are aware of when to turn it off and correct manually. I leave it default off, and turn it on for a few seconds to get close to trim, then turn it back off. Fine time I do manually.
