Tokina 11-16 is a good lens, but the Sigma 10-20 isn't bad either.
Just suggesting something else besides the obvious.
I've used both, Tokina is slightly sharper and does not have as much light falloff, but discerning that difference required serious pixel peeping. Tokina has a bit more flare and a tad bit more distortion also required pixel peeking.
I've seen bigger differences between the same lenses then what they produced.
Also for landscapes the extra stop doesn't matter that much. (Unless you go for night but then again it's just one stop.)
And the big-bang: the Sigma is cheap.