I used to prefer Pinball Arcade over Zen Pinball because I loved playing actual tables that I remember from my youth. That ended when I couldn't get any of my purchased tables to show up (for the umpteenth time) in that godforsaken app. I thought the physics and whatnot were great, but the wrapper to switch tables and their constant failure to recognize tables you've purchased along with losing your scores was infuriating. I haven't checked it out in a while to see if it's gotten any better, but I probably should now that I have a new iPad. (Yes, I bought a new ipad solely to play Civ VI).
My favorite table of all time is Star Trek: The Next Generation. It was at this skeevy bar that my friends and I used to hang out at in college. One of those bars that no one went to because it wasn't cool. We didn't go there all the time, but we did to get away from the crowds and bar scene every now and then, and I'd spend my time dumping quarters into that table. Love it, and kickstarted it when they were trying to get it into Pinball Arcade.
I also love Bride of Pinbot and Twilight Zone (one of the guys in my game group has a pristine working Twilight Zone table in his basement). I generally enjoy tables with a good story and missions that you can figure out without panicking and that have some connection to the theme other than "hit this target for no reason". I want to try and figure out the missions and find the end game rather than searching for a quick-hit high score combo. Thus, I should like a lot of the Zen tables...I played the Thor one a bunch and enjoyed it quite a bit, but it fell to the wayside once PA got ST:TNG.
Oh, and I suck at pinball, by the way. Not sure a tournament is my thing only because I'd be out of it in such laughably short order. That said, I do enjoy playing it, so I'd be willing to try whatever you can think of.