The original and Europe versions differ HUGELY, it's not just a different board.
The US version is the simplest formulation of the game. It accommodates up to 5 players, I believe, and it'd be a great one to play with non-boardgame-obsessed family members, including the old and the young. It's still got a great deal of strategy and depth to it once you know where to look, but it won't turn off anyone who can handle Monopoly, Scrabble or Risk. (The 1910 expansion adds less unwieldy cards and a few new variants, but keeps things maximally simple and elegant.)
The Europe version is also good for large groups but takes the complexity level up a notch. Now you have to deal with concepts such as tunnels, ferries and stations, which severely alter the dynamics of collecting cards and claiming routes. It's a more gamer-y Ticket to Ride which I would probably recommended over the US version to anyone who plays with mostly hardened gamers. The 1912 expansion offers variants at a similar complexity level.
I haven't played the Marklin (German) edition but I believe it's got extra twists over the US version that probably put it on about a par with the European set.
I have played with the Nordic Countries edition and it's my personal favourite. The caveat here is: it's only for 2 or 3 players, so don't get it if you need to regularly cater to a larger group! It is even more complex than Europe, with a lot of exceptions to the normal rules that are pretty hard to grasp on the first play - but it's perfectly balanced and my wife and I come back to it again and again. The Switzerland game is another 2-3 player outing, and again I haven't actually played this one, but most of what I've seen written about it suggests that most people prefer Nordic Countries.
Hope this helps!