Not that PP cares about my opinion as I certainly can't be a customer of theirs anytime in the foreseeable future...
Still, I think the Geneva Seal would look better than their own stamp. The Geneva Seal sets standards that any number of companies could try to achieve, while the PP seal is just for Patek Philippe. Doesn't their brand name serve the same purpose? Who really cares if a company comes up with a logo that says they're meeting the standards that they created?
Yes, I'm aware that many standards are influenced by the groups that would benefit the most from them. I suspect that's true for the Geneva Seal, certainly it's true for COSC and there's the farce of being "Swiss Made"
What would be more impressive would be to have some independent body come up with a program that graded the watches on a number of criteria and awarded different scores or levels. It should be designed so that the minimum score is still meaningful, but the highest levels are absolutely unattainable by anyone using the current levels of technologies and knowledge. Let this be something that a company strives to achieve over many years, not just another meaningless marketing gimmick used to increase profits...