I assume you are talking about the models with Image Stabilization.

Sigma also makes a 18-200mm lens that does not have Image Stabilization.
You can find that one for under $200.

Any lens that has a range of 18-200 will have problem areas.
Such as noticeable barrel distortion at 18mm.
Both lenses exhibit that.

The reviews of both lenses show that there is not a lot of differences between the Sigma and Nikon lenses.
The differences are not enough to give either lens an edge over the other.

Reading user reviews, the owners of both lenses like their particular brand choice.

From what I see, you could toss a coin and be happy with whatever comes up.