I have a very limited understanding, but the impression I got is that VCs typically have short maturity dates and thus are riskier in nature, whereas PE funds typically have the luxury of biding their time. How this is structured, or why exactly is beyond my ken.
So upside being, VCs are incentivized to encourage larger risk taking than what would be otherwise optimal from the perspective of a bootstrapped founder.
The bootstrapped founder, on the other hand, doesn't necessarily need to exit the investment in those 8-10 (or shorter) years. There are, of course, serial entrepreneurs for whom that is their goal, and for them (as the article points out) their incentives are aligned. For "lifestyle company" founders (not meant to be disparaging), an exit may not be necessary at all. The key differences are time horizon and exit.
The most typical arrangement is 20% after 1x in LP distributions, with some variation in what are called hurdle rates (that is, different percent carried interest at different multiples or IRRs).