I don't know what the percentages are, but a small number of anglers are certainly the ones that catch the vast majority of the biggest fish on a regular basis.
We often hear about an inexperienced fisherman going down to a dock, or heading out randomley in a boat and catching a large fish, but if that big fish isn't sitting at the end of the dock, or under his boat, he doesn't know where else to go or what to look for to find that biggun.
An experienced fisherman will understand the habits of the fish he's after and will have a plan in his head before he even leaves home in the morning. He'll know where the fish SHOULD be holding depending on the time of day, the weather and even the different seasons.
It takes no skill at all to fluke into a big fish from a dock or find one sitting under your boat wherever you happen to drop the anchor, but it DOES take skill to know what to look for and where to go and find big fish consistentely, and that's where many fishermen fail, because they don't know what to do when plan "A" fails
A small percentage definetely catch the most and biggest on a consistant basis.