For airliners, there is less room for error caused by the pilots (but it still happens). In General Aviation, the accident rate is more than an order of magnitude higher per mile (FAA has the data on their site) and by far in most cases it is pilot error, even if GA planes are less reliable. The official statistics are not very accurate because the GA accidents are investigated with less rigor, there are no black boxes to record what really happened and the pilots lie about the real cause (in more than 50% of the accidents I personally know).
It is hard to prove all these, but some data exists on the FAA site, the inside info will never be public anywhere to consult. By inside info I am talking about the real story told by the pilots that had the accidents, in small communities people talk very openly about it.
LE. I mentioned General Aviation because I know pilots with over 10,000 on B737 that died flying smaller planes or not able to fly at all smaller planes.
Sorry, trying to clarify but there is too much to tell for a full picture. In a B737 you are not allowed to do most maneuvers you do when flying a small plane or a fighter; not necessarily acrobatics, but even more basic things like stalls, spins, side slips or flying without engines, which is something I regularly do to maintain my proficiency. That means 10,000 hours of limited, routine flying does not make a lot of difference, especially when you get into an incident that is outside of the routine.
Good pilots vs bad pilots: some pilots that I know can fly visual without any instruments, knowing the plane and feeling the plane. Many others are barely flying straight if you mask their artificial horizon and VSI.
A simulator is to flying what porn is to sex: a simulation pretty far from reality. I had a lot of simulator time when I first flew a plane, it still took me 8 hours to be able to fly it in real life and that was a very simple 2-seater trainer.