What returns does private equity need to produce to be "good".  IMO, it isn't an easy question.

It is easy to simply compare to the S&P 500.  But the US has been the best performing stock market  and large caps (which is the S&P) have also performed the best.  There is no guarantee that either of these will continue.  And if you are an asset manager making such a concentrated bet would be not wise.

So you need to compare PE to more global returns and more than just the large caps.  

OTOH, PE is illiquid, although the secondary market is pretty big at this point.  You also don't have a clear view of cash flows although large investors can use leverage to solve this problem.

Below is an analysis from Hamilton Lane.  Of course they are a huge player in private markets so take it with a grain of salt.  And past performance is not a guarantee of future returns...