This will be dependent on a number of factors such as if the stock is widely held, are there majority shareholders, is the company in distress and what regulatory approvals are required? A privately held company with a single shareholder might be more challenging if the price they demand is not reflective of fair value, compared to a public company that may or may not be widely held but where the board has a fiduciary duty to evaluate an offer.
I think there are complexities in each type of company. For example, in some countries private companies don’t have to make their accounts publicly available, making an initial approach that much harder and due diligence potentially longer. One may end up doing quite a bit of expensive work with an offer being rejected due to inflated expectations by the current owner. The cultural integration may also be more complex, especially if acquired by a public company.
On the other hand, acquiring a public company will be ‘very public’, so to speak, with more regulatory and market scrutiny, which can damage both companies if doesn’t materialize or succeed.