I've owned PoTC since 2018 when it first came out. It's one of my favorite games. Here's a quick and dirty category comparison in terms of what I think is better on which game:
Layout = Godfather. I personally enjoy shooting this one more. It's faster and shots are smoother. The better flipper strength plays into the enjoyment and I'm loving the diverters. It's worth noting that I generally don't like widebody games, so it helps that this isn't a widebody.
Sound/Music = Pirates. Sound and music is good in GF, but David Thiel crushed it on pirates.
Lighting = Godfather. JJP always impresses with lighting, but the addition of the new light bar (whatever it's called) has taken it to the next level. I thought it was odd to include it games outside of GnR, but seeing it on this game in person has changed my mind. I love the health bar for the bad guy.
Toys = Pirates. The moving ship on Pirates is badass. So cool, so thematic. The spinning disc is OK, and the chest, despite not moving, is nice. The bad guy on GF is "OK". I like the spinning disc to beat him up, but Pirates takes this one.
Rules = Godfather. Love me some multipliers and GF gives more options here. I'm also a huge fan of the "push your luck" mechanism in deciding whether to cash out or keep going on modes to build a higher score. Modes are distinct and more interesting. The numerous skill shots are also nice.
Theme integration = tie. Hard to give it to one or another. Both feel like 50% movie, 50% (generic pirate/mob game)
Art = Godfather. The playfield art on pirates never really did it for me. In contrast, I really love the playfield art on GF. It's perfect IMO. Cabinet is great as well.
Score: Pirates 2
Godfather 4
It's early. It will be interesting to see how I feel about this game months from now. I often can look at a game's individual parts, but as a whole, prefer another game. So even though GF wins these categories, months from now I may still crown Pirates as my favorite. Although, at this moment, it's GF.