Any sources on these claims?
There are great hedge funds that outperform in the long run, like Rennaisance Technologies managed by Jim Simons.
But the vast majority just return market returns over the long run before-fees and therefore below market returns after-fees. The hedge fund format is definitely outdated and needs to include more asset classes than just the traditional long-short equity-bond portfolio, but I don't think that day traders can do better than them on an after-fee basis in the long term either.
Renaissance Technologies is an HFT algorithmic fund. AFAIK those trade in darkpools rather than standard markets accessible to the general public. Which puts it outside the category of how a normal hedge fund could be expected to perform. I think most big HFT and algorithmic trading gains came early on with arbitrage trades, before HFT markets became as heavily saturated as they are today. Where there is much more competition to execute the same strategy of trades.
Profitable day traders would be those affiliated with the gamestop bull run or the big dogecoin pump. Those types definitely outperform the traditional hedge fund. I think most would agree with that? There are some I've seen do well day trading penny stocks.
Hedge funds have traditionally been very lucky if they succeed in breaking 5% year over year gains. The average successful day trader can beat 5% annual gains, easily.
another thing I forgot to mention is, its much easier to buy and sell assets. Get in and get out. Trading small sums of money. Than it is with large sums. That's another big advantage that daytraders have over hedge funds which manage much larger sums.