Tokina 11-16/f2.8 thoughts?

I recently bought a Tokina 11-16mm f/2.8 for my Nikon D90, but I had also been considering the Sigma 10-20mm f/4-5.6. I have 30 days to return the Tokina if I so choose. The Tokina appealed to me because of the extra speed of course. I wanted a wide-angle for a trip to the Grand Canyon, but I think it likely I'll be using it for indoor and street photography, as well as occasionally in our local community theater without flash, so I figured the faster lens was worth the extra money as well as giving up some range at both ends. Any thoughts you'd care to share? Does my thinking here seem sensible? If you happen to have this Tokina lens, in what types of situation exactly do you find the extra speed to be an advantage?

My other lenses are an 18-200 f/3.5-5.6, a 70-200 f/2.8, and two inexpensive primes: 35mm f/1.8 and 50mm f/1.8.