Better at Acquisitions – Private or Public Companies?

If we go by a single success criteria, “holding on to acquired businesses longer”, would this not be private companies? Is there data to test this difference between public and private?
When I see the number of times public companies sell on acquisitions relatively soon after the transaction, I wonder if they do not give the project enough time to succeed, or were expectations simply too high, i.e. they overpaid.
If its you own money, is integration done better?
I have the intuition that its a combination of; longer term outlook, less short term profit pressure, but often that private companies acquire at sensible multiples as they hoover up selloffs from unloved public company divisions. They get bargains as they can live with lower margins as long as the cash flow is good. But would love to see the data.