I don't think experience trumps training, but it depends on the experience gained and the training recieved.
Take what happened in Mogudishu in '93 between American forces and Somali militias. Throughout the fight, even though they did have air support (especially at night), the Rangers & Delta guys were outshooting their opponents consistently. This is pretty well documented by eyewitnesses from both sides.
However, what is often overlooked is that the Somali militiamen, by and large, would have had much more actual combat experience, or experience with gun violence in general, than any of the American soldiers. They grew up surrounded by etreme violence their whole lives. Gunplay, and gun violence is second nature to them, and still is, yet they recieve no real training and paid for it severely in that encounter.
If you don't train to properly use your weapon, your experience will mean little against someone who is properly trained.