The biggest difference is not the morality of the management of the two types of companies, but the type of business they are into.
Many private companies are growth businesses. On the opposite side, private equity targets businesses which are stable, but not growing or declining. PE looks for products which have high cost to switch or products with no alternatives.
So when private equity buys the business they extract money in 3 ways:
- Raise their prices. This is similar to the public companies, but they do it more aggressively, because their customers don't have a choice. For reference see, what VMWare did after it was bought by Broadcom (Broadcom is a public company which acts as a private equity).
- Reduce costs, via layoffs and cutting smaller products. Also done by public companies, but the difference here is the magnitude. It is quite common for Private equity owned companies to have several years of 20% layoffs, until the original workers are completely replaced by workers in cheaper locations. Or not replaced at all which leads to a worse service.
- And finally the third way a private equity extracts money from the acquired company by providing "services". Employees from the PE company are elected on the board of directors of the acquired company. A PE executive can become a CEO of an acquired company. PE companies have satellite companies, which provide legal, administrative and financial services to their companies.
On top of that the acquired company has to pay the loan which was used to be acquired.