New World plays much like Carcassonne. The main new mechanic is the two surveyors, one of which moves one "column" of tiles to the west each time someone scores points. All followers that are behind the rearmost surveyor when it moves are returned to the player. This tends to focus players on starting and finishing one feature before someone else scores. An additional aspect of the surveyors is that if a follower is in the same column as a surveyor when the feature the follower is on is scored, the player gets 4 bonus points. If both surveyors are in the same column as the follower, the player gets 8 bonus points. This means that if you can pull off a quick score on a tile in the same column as both surveyors, even a simple 2 point score can net you 10 points. I also like the "east coast" starting board for starting the game instead of the specific square used in the previous games.
If you are a fan of Carcassonne and are looking for a slightly different twist on the game, I would recommend this game. Unfortunately, because the art style is different, the tiles in New World don't fit with tiles from the other Carcassonne games stylistically. If you aren't concerned about the art, the features might still line up, so you might be able to use them. If you are looking for a wildly different take on the game however, you will be disappointed, as New World is at least 90% the same as the original Carcassonne game.
If you have never played Carcassonne before, I would recommend that you get the regular Carcassonne game instead. If you like it, there are many expansions that fit with that game.