Quoted from Jediturtle:

Man, that's a tough call. Both are fantastic and probably top 5 of all time for me. I went through a brief phase where I fell out of love with JP and sold it, but thankfully I snapped out of it and got one back. Not sure what I was thinking, because this game is amazing.
AIQ is a slightly better layout to me. The shots are a bit easier overall and can lead to flowing a bunch of unique combos together...more than any other game I can think of. JP is no slouch there, but the shots are tighter and the flow isn't quite as prevalent. Both have some great "sharp shooter" type sniper shots as well as all of the flow/combos. Both have very unique layouts, not a copy or even really reminiscent of any other game. The pro/premium divide is bigger on AIQ, with the changes being major game/shot changes, where-as JPs are mostly eye-candy with minor affects on play. To me the AIQ premium upgrade was well worth it, but I am completely satisfied with JP as a pro. Many do disagree with that and consider the moving dinosaur to be a must-have, so YMMV there.
Rules are great on each. They each have some pretty simple surface code for beginners to have fun with, and then as much of a rabbit hole of depth as you could possibly want. Lots of strategy if you choose to utilize it, but you can ignore it and just shoot the blinky stuff and still have a blast. I have a really hard time choosing here. JP paddocks can seem a bit repetitive, which is part of why I sold my first one. They started to feel like a slog. But on further play, the unique movement of each dinosaur is really cool and thematic, and concentrating on keeping a good rescue streak going as opposed to just blasting through them quickly makes them much more interesting. AIQ does not have any sort of repetitious feeling as each of the gem quests are very unique in how you play them, and you can still choose to blast through them ASAP or concentrate on maximizing scoring, bringing in portal locks, etc. For that reason I would say AIQ has a slight lead from a "main mission" stand point. Both have plenty of "side missions" to do as well, and to me this is where JP really shines. Control Room modes are unique and fun, with slightly blah A/V. The T-Rex modes though...those are AWESOME. Pure adrenaline and heart pumping, so much fun. Just these side modes offer more depth than some entire games have. AIQ doesn't really have much that compares to these modes, instead having you collect the Avengers to progress through Soul Gem (which is crazy unique and amazing), Black Order Multiball, and Battle Royale. All very cool modes as well. Both games offer some very interesting strategic decisions. JP with your path through the map, perks for the different dinosaurs, and to fight or skip the super-predators. AIQ with the unique gem perks and how they interact with the various shots and Avenger levels. Great stuff on both, and again if that seems overwhelming they can be ignored and played in a much more simple way. Both have awesome wizard modes, as well as many other small modes (Hulk Rampage, Gamma, computer modes vs Pteranadon, Smart Missiles, DNA combos, etc). Both have some fun multiballs. AIQ's Thor and IM are slightly more generic feeling (probably partially my own lack of understanding them so far), but it does have the advantage of the portal lock system and the ability to turn every gem quest into a multiball. That's awesome. JP on the other hand has more unique feeling multiballs, which are a bit more fun to me. Spelling CHAOS for that multiball especially is a blast. Both have a bunch of very cool, unique skill shots, but JP definitely pulls ahead with it's insanely satisfying multi-level combo skill shot. I've only hit the 4 way twice and the MXV once, and there is no greater feeling in pinball. I am surprised there isn't a similar combo skill shot on AIQ. So...all that is a really long way of saying...they both have amazing code. I would almost call it a wash. If the paddocks were a little more unique feeling, JP would probably be the clear winner, but that is really the only place I can fault it.
A/V assets are pretty close. I truly enjoy both games as-is, but there are many that find them both lacking. Neither game is based on the movies, and therefore animations and voices are not what most expect them to be. I think they did a great job on both of them though. I love the dinosaur animations, sounds, and music on JP, though some of the voices are not great. AIQ has really beautiful "motion comic" style animations which I absolutely love, but some do not like them since they are not full motion. Music is a bit more generic than JP in my opinion, but not bad at all. Voices are fine for the most part. Maybe a little jarring when you are used to how the movie actors sound, but really not bad. AIQ has a more serious tone, not having much humor present. JP is slightly lighter. Again overall A/V to me is a wash between the two.
Art is pretty easily AIQ. Zombie Yeti is simply amazing and everything he touches is gold. I actually really like JP's art as well, especially the cabinet and translight (I have a pro that I love the look of, I am not as big of a premium fan, but the LE is gorgeous). The JP playfield is a big step down, especially the odd decision to have Nedry's ugly mug featured so prominently when there are no other actors anywhere else on the machine. Replacing him with a triceratops would have been a HUGE improvement. Don't hate it, but don't love it. Overall, AIQ takes it here.
So yeah...not sure that helped at all. Both are amazing games, and you can't go wrong with either. While I find them pretty much neck and neck, it does seem to me that JP is slightly more universally loved while AIQ may be a bit more polarizing. The depth and strategy seems to scare many people away, but it really shouldn't as that first layer is actually quite simple and still satisfying on its own. I would actually say AIQ is slightly more intuitive to people stepping up to it for the first time than JP is. Either way though, both games have a ton to offer.