Is it worth buying a 10-20mm lens?

I currently own a Nikon D5100 which came with a 18-55mm lens. My question is, is it worth it to purchase a 10-20mm lens. I'm planning a trip to the Philippines next month and will probably be taking many landscape shots. The 10-20mm lens is around $400, so i'm just not sure if there's that big of a difference between the lens i have now and the 10-20mm. Any help would be appreciated.

I have a Tokina 11-16mm lens along with a 18-200mm lens. I use the 11-16mm lens for vacation and cruises. It is well worth it for landscapes and internal shots of buildings.

The better lenses are:

Sigma 10-20mm
and
Tamron 10-24mm -

personally, i would say you'd be better off with an 18-200mm lens for travelling… Then you don't need to worry about moisture and stuff getting in the body…

Sounds worth it to me if you like wide landscape shots (I'm guessing 10-20mm is noticeably different from 18-55). But if you can test one out before you buy, that would be ideal.