There is another version of the Sigma 10-20 with constant f3.5: Sigma 10-20 F3.5 EX DC HSM
But this will be more expensive.
To be fair when using a wide angle lens, you're more likely to be taking a shot of a whole scene rather than a specific object, so you probably won't be needing a narrow depth of field.
The Sigma is definitely the more popular lens.
But have you looked at the Tokina - AT-X 116 PRO DX 11-16 F2.8 ?
Tokina aren't as big a name, but make good lenses, so can be cheaper.
Here's one on ebay dirt cheap at the moment.