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.
New York times is a lot harder, but the crosswords are on completely different level, quality-wise. There are no clues like 'Please take me to _ _ _ airport' (answer: The). Since it all comes from actual NY Times newspapers, many of the clues are pretentious and try to be too clever for their own good. It's worth suffering, though, in order to play some truly challenging and satisfying puzzles. Unlike CrossworDS, which I do like, it's not uncommon for a NY Times puzzle to take one an hour or two to complete. Still, if the difficulty is too high, you always have the option of sticking to the Monday and Tuesday puzzles (The puzzles get progressively harder as the week goes on, topping off at the Sunday puzzle).
The ranking system in NYT Crosswords is stricter than the one in CrossworDS, too. Whereas I've never seen anything below an A on CrossworDS, my NY Times rankings have been all over the place.