Having owned and now sold both I would go with Lord of the Rings. Pirates has more shots and toys but its ruleset is severely hampered by a lack of licensed assets. All of Lord of the Rings main modes, mulitballs, and wizard modes are filled with assets from the films which are each brilliantly told as their own mini story.

Pirates is an amazing pin but its main modes (the chapter modes) feel dull in my opinion due to only ever hearing Gibbs callouts versus multiple actor callouts timed to animations unique to that mode. All of Pirates multiballs are also very generic with no stages and only the same callout voice ever being heard. Pirates does have 5 wizard modes but again only Gibbs callouts and for some reason they are only 1 ball which makes them disappointingly short.

If JJP had the rights to use actor video and actor audio across all 5 films Pirates would easily go down as the GOAT in my opinion as it has everything else going for it.

I would compare chopping wood to pinball as performing the same task over and over again. MET is famous for this besides the Crank it Up modes which are unfortunately only unlocked much later in the game. Want to start a multiball? Hit the same shot over and over again. Then most of the multiballs play the same way. Same goes with ACDC with its song modes and multiballs often requiring a single shot to be hit again and again.

Other examples are games filled with "super modes" that have you hitting the same shot over and over again. Games filled with "super ramps", "super pops", and "super bumpers" type modes come across in my opinion as filler modes with little value compared to well flushed out story based modes. The same goes for modes that have a player just hitting a ramp or orbit 5x, then 10x, etc.

A ruleset such as that in LOTR is the complete opposite of above and has modes that require the player to work the entire playfield in interesting ways while telling a themes story through unique mode animations, music, callouts, and sounds. When a game then implements that type of mode design into multiballs and wizard modes that have multiple stages you get a ruleset that makes players coming back again and again. Those are a couple reasons why I think LOTR has been so well regarded for this long.