I have seen both in person quite a bit, and owned a kind of similar Patek + the Tonda chrono.
I don't love either. IMO the Parmigiani looks like the land of missed opportunities for sharp internal angles, and because of that, I greatly prefer the solid dial ones. The new ones they just released with solid dials look great imo.
On the patek side...not huge on the aesthetics...would probably go with a different PP in the same price range.