My instinct and observations tell me private sale. But try to make that a competitive bid. It's not hard to identify dealers, call them all. Private sale also sounds more attractive if that is private sale now versus auction sometime next year. Lots of variables in the world, who knows how much or little money will be sloshing around next year.
While I've not followed Panerai auction results super closely but my recollection has been results have been soft. You should check this yourself, methodically. This is a big factor to consider.
If you are inclined to take the bet on auction and if Phillips are telling you they are going to push really hard for you on marketing etc for the collection, and can give you some level of comfort as to min price achieved (does the watch auction world even do that), then perhaps it's worth a punt based purely on the Phillips marketing machine.