It's quite simple I would say:
Low effort, market-rate returns: Index-Investing
High effort, uncertain returns: Individual Stocks
I am of the opinion that if you spend a lot of time, and you have the capacity to properly analyze a company and sector, you can pick stocks that outperform the market, if you are in it for the long haul. This is mainly due to picking healthy companies, in sectors where you expect the market to behave differently than the general opinion.
At the same time I am also of the opinion that even if you spend a lot of time and you have the capabilities, you cannot outperform the market with shortterm or daytrading stocks. The derivative trading houses and algorithmic flash-trading is going to take any obvious advantage out of the market before you as an individual investor can pick them up.
All in all, if you have the skills, the time, the drive, I think it is possible to beat the market with a select few individual stocks. To see if this is a better investment, you'd have to take into account the starting bankroll, the amount you'd add each year, your opportunity cost, the rate with which you beat the market after transaction fees.
Taking a $200k roll, a $20k yearly deposit, a $50/hour opportunity cost, and beating the index by 3% (10% instead of 7%), it still takes our handpicker 10 years before he outperforms taking the $50 opportunity cost and just depositing it in an index fund. This is given you take 1000 hours learning and figuring it out, and 100 hours yearly maintaining your portfolio.