I currently have a LAH and JD (2nd JD) and owned a Shadow for about 6 months in the past. You can't go wrong with any of these games. What game you should choose comes down to what theme you'll like having around the most, as all have a bunch to offer in gameplay. I voted for JD, as I've owned it the longest of the 3 and can't see myself parting with it again.

JD has the most unique layout/shots of the 3. The shots exclusive/easiest made from the upper right flipper are a blast and make the game feel huge. While it can feel a little slow compared to standard (non-widebody) pins, it is still pretty fast. I really like the central location of the drop targets and their role in starting multiball.Best art package of the three games by a mile. One of the few games where the PF, translite and cabinet are all equally well done. Topper is awesome and ties it all together.

LAH is still brand new to me, so I can't comment too much on what it has to offer. Just listing the toys/mechanics on the game sells it, though. 3 huge magnets, the crane, a row of drop targets, 3 scoops, 2 captive balls, return plunger (can't remember commonly used name. Same as raptor kick shot in JP). It is a truly packed playfield in the best way possible. The modes in the game (and there are a ton of them) make great use of every shot/toy on the PF. Feels complete and well thought out. Easily one of the best games by Data East or Sega. I am a huge Schwarzenegger fan, so the art package doesn't bother me as much as it does most people, but the translite to the game is truly hideous. The cabinet art is mediocre. PF art is busy but really detailed, I wish the whole game was done in it's style.

The Shadow's player-controlled diverters and awesome mini-playfield are what makes or breaks the game. I really loved both and found it an awesome game and regret selling it. A vicious game and the most difficult of the 3. No pop bumpers and a really fast layout means you have very little breathing room. Unique theme that you'll either love or hate. Ugly translite, great cabinet. PF art reminds me of BSD's, middle of the road overall.