I always like to say that we live in an exponential meritocracy , where your accumulated merit enhances your ability to accumulate more merit, eventually resulting in a small minority rapidly pulling ahead of the pack. Goes with the old adage: turning $100 into $120 is work; turning $100 million into $120 million is inevitable. Perhaps we need a linear meritocratic function.
"The rate of return you get on your capital increase as your capital increases" is the most interesting thing I've gotten from Piketty's book, and it's definitely been true for me.
However, at 10M vs 10B, the 10M investor is much better off. Liquidity becomes a real concern - there's just not that many assets or stocks that can support that kind of allocation.
Small, nimble investors can usually outperform large funds simply by being able to fully enter into positions where larger funds couldn't.