I've heard NYT has very good crosswords, but they are very difficult. If you are a crosswords buff and like a challenge (and also know a lot of history and world news), then NYT. I also heard that the hand-writing recognition is quite good.
If you want an accessible crossword game with a few extra features, then get this game.
To make sure, you could try a NYT puzzle in one of their newspaper to see if you can do them (all of the games many puzzles come from the newspaper), and you could also try the download demo of Crosswords DS at a Download Station (at Walmart, EB Games, etc,) or off the Nintendo Wii's Nintendo Channel DS Download Centre. That way you can really tell which one you want.
I have played the Crosswords DS demo, and I think I might buy it because it is quite fun. I haven't played NYT Crosswords though.