For (most) management. Absolutely do NOT do this:

"I’d wait for a more private setting."

Only do this IF you think management is well adjusted human being that is not ego driven. I leave it to reader to decide exactly how much of management falls into that bin.

If management is not, they will know that you are a threat to them and work to undermine you and get you removed. If you provide feedback publically they can less afford the reputational hit (if you're correct in your publically aired assessments).

In either case you must play nice with your coworkers and subordinates.