how does an "investor mindset" differ from a "CEO mindset"

Having been on both sides of this...in my own experience, the general differences have far more to do what the roles & responsibilities of each role entails (i.e., experience), and what is required to move up in each of the respective career paths (i.e., the achievements and accolades over time), more so than potential or general competence (notwithstanding individual propensities to be better at one vs. the other).

Good PE investors are "generally" great strategists, but not great at execution (lack of ops experience) and most of the time terrible people managers (high finance does not "lead" people nor do they really need to be great leaders, they tell people what to do in exchange for high compensation). CEOs are great executioners, but not as great strategists. To be clear, I'm not insinuating CEOs are bad at strategy, they have to be good at strategy if they want to scale a business. CEOs just simply don't see as many business models and/or have the time to think high level strategy relative to PE people who spend all day evaluating what are "differentiated business models" and how to maximize exit value (and exit value isn't always the same thing as long-term value). Whereas CEOs spend some time setting the strategy, but once a strategy is set, CEOs spend an inordinate amount of time managing the people and business processes to achieve the desired strategy; and occasionally review/revise strategy. PE people have very little knowledge of what is actually required or happens in the day-to-day to build a great business, they simply do not see this side of business ownership (even the most hands-on PE firms; and usually "hands-on" means there are operating partners that are hands on, not the investors). Instead PE people will talk about what do great businesses look like and what levers to pull (at a very high level), but don't know how to get there, how feasible it is to get there, how to prioritize initiatives given the limitations on resources/time of the business, etc.

To one of the other posters point, in theory there shouldn't be a difference. Having Ops experience can be incredibly beneficial to being an investor, and vice versa. But the roles and responsibilities of each career path dictate what each person is spending most of their time and attention on; and at least as it stands today, there just aren't a lot of opportunities, or it doesn't make financial and/or career sense, to jump around between the two. Because of carry, very few senior investors leave to go be CEOs (although we'll see if this remains true in the future given the financial incentives of PE are declining for future generation of investors). And PE firms typically do not hire CEOs to be investors, they are hired to be operating partners (rightfully so given a CEOs experience).