On a lens as wide as the Sigma there is going to be hardly any difference between f/3.5, f/4 or f/5.6 in terms of practical DOF. for background blurring, I'd find myself using it at 20mm rathern than 10mm, despite 20mm being a stop slower, it was easier to blur the background. the f/3.5 will be slightly better in low light, but really it comes down to splitting hairs at such short focal lengths.
The following photograph was taken with the variable aperture Sigma in almost pitch black darkness:
...hand held.