As mentioned above, The director's cut is more technically advanced. This leads to a lot of increased ambiance For instance, fog and lights move and seem more real in the beginning, and shadowy ghosts can occasionally be seen which makes the game a little more "scary" than the original version. There are some added interactive elements like video presentation screens.
A lot of puzzles are changed: A couple ones that were too hard are simplified, while some puzzles were made harder. Many of them simply have the answers altered so people who played the original won't breeze through it. There was an area in the original game that wasn't really used and so the accessibility of certain areas has been changed to more rely on that.
Some very minor story elements were changed: a museum multimedia exhibition had its dialogue changed, but I don't actually remember the differences. There was an "unrelated" ghost story included in the original version that was replaced with another story about the lighthouse in the game. This might be because some people reported their TVs seeming to turn on when they were at that part of the game (it seemingly happened to me once, but I just finished reading it during my recent play through and my TV is fine so take all those accounts (including mine) with a massive grain of salt.)
They also added more interactivity with certain ghosts through dialogue trees, which in my opinion ruins some of the mood of those segments but some might like it.
Overall, I'd say you should play the Director's Cut version first, as it is the creator's preferred version and it has more content, then if you end up loving the game play through the original version on a subsequent playthrough.
Post edited October 28, 2015 by DrNilesCrane