As far as I am aware, Mack rides do not do any theming apart from the themed boats or vehicles for their rides. They do not make themed entertainment.
Mack rides are the fabricating company run by the Mack family. Their other companies; Mack one and Mack animation absolutely do engage in design work, including concept design, scenic artwork, AV design , show control etc) and were involved in some of the designs for Piraten en Batavia rebuild , after the awful fire a few years ago.
They don't directly manufacture the theming, but do the design work, architectural schematics, and are involved in the electrical/mechanical setups, and creative guidance during installation.
As great as the ride was and it was great, the ride was no where near the quality of the Disney Pirates rides and never was. Not even close. They are in a league of their own, especially the one in Paris. I am guessing you have never ridden one? If not, you should, they are truly amazing attractions.
Everything from the audio, set design, lighting, FX and animatronics are far far better than anything that was ever at Drayton.
It is no surprise, you get what you pay for. You could probably build the whole of Pirate Adventure from scratch, for the cost of a single Animatroic from the Disney Pirate rides, specifically the auctioneer, which runs into many millions per figure.
Even when you look at construction pictures of the Disney Pirate rides, everything was built out of much higher quality materials, such as concrete and steel for the buildings and rock work, materials that are designed to last. Drayton's Pirates was basically made almost totally of OSB chipboard and cheap molded plastic - no doubt all rotten and degraded by now. It certainly was when I walked around the ride at Drayton 10 years ago.
If you factor out the animations and control systems, I wouldn't say that Pirate Adventure and POTC are that different in terms of detail. Both used a similar Georgian style for most of the buildings, and a similar number historically relevant props for each scene . And the set pieces for both rides used mainly PVC / ABS polymers, hessian backed plaster , steel framing underneath, and fibreglass too, so there is not much difference between the two in scenic build quality, in all honesty. Both rides had bespoke soundtracks ; if anything Pirate Adventure had more in terms of musical variation, whereas POTC was a little repetitive in the yo ho leitmotif, but had more in terms of dialogue. If we're using POTC as it is now, then the lighting / dimmers/ flicker units the ride currently uses don't look natural in the way that the ride used to . There's an overuse of digitally controlled RGB LED strips in present day POTC too; which have a lower color rendering index. To be honest , if we are talking about the ride as it is now, there's tonnes of criticisms you can go in to (the silly removal of original scenes for silly reasons, constant film franchise references that make it feel more like a POTC film advert, the projection mappers)
The big difference between the two rides, as said, is
obviously the animations. But hyper-realistic animations , as impressive as they are from a design standpoint, don't always mean a more immersive experience, in my opinion. In fact it can look rather unusual to see such lifelike figures unable to walk around and being in stationary positions; whereas this is less the case with the cartoonish figures you had in Pirate Adventure. Lots of movement also gives away all the game as to what's going on. Whereas the more 'still frame' or 'basic' animations can be better for immersion. The Kingmaker in warwick castle is a perfect example of how some of the best immersive experiences don't necessarily require a lot of movement. Your imagination fills in the gaps, using the visual stillframe detail provided. Personally, I quite liked like limited movements and cartoonishness of Pirate Adventure for that reason too.
POTC was brilliant in its original innovative 20th century form, and still remains a great ride, and owing to its budget has a certain set of advantages over other themed rides, but I disagree that it is 'objectively' better as a ride than Pirate Adventure, or that it is necessarily more immersive, especially if we bring in the rides modern day flaws. I'd say it very much is subjective, and a matter of opinion