Private equity deals usually involve a significant ownership stake of the company (higher than 20%, maybe even a complete buyout) and therefore often come with board representation, financial reporting and access to financial information, protective rights on corporate actions (like mergers, fundraise, etc) and exit rights. Pre-IPO deals are usually purely financial in nature and involve a lower stake ownership. These deals don't normally involve any special rights apart from exit rights.
However, there can be no standard rights and protections apart from those mandated by law. These are all variable and subject to negotiation between the company and the investors.