I guess I'm one of the ones that errs on the side of minimising public embarrassment whenever possible. Because no matter how nicely we couch it, the message behind most critique is "you're doing it wrong", and that tends to make people defensive. Putting it in a place where anyone & everyone can see it only compounds that defensiveness, in my experience.
That said... if it's a problem with a specific profile, I will put a public message on that profile (rather than the PM's personal profile) and try to make it impersonal, e.g. "This profile has X issue" rather than "You did something wrong here". If it's an overarching style issue or involves multiple profiles, I'll take it to private e-mail and follow up with a public message, e.g. "Hi, I sent you a private message about X. Did you get it?" - that way, others can see that the issue is being addressed.