From what I've read, the only advantage of the f/3.5 version is that it's 1/3rd stop faster at the wide end, and 1 1/3 stop at the long end.
However, the f/4-5.6 version is cheaper, lighter and uses 77mm filters (HUGE advantage imho).
For a sharpness comparison see here: http://www.the-digital-picture.com …omp=0&FLIComp=0&APIComp=0
There's not much between them wide open at the wide end. At 10mm f/8, the f/4-5.6 version looks a TINY bit sharper, albeit with what looks like more distortion and vignetting. I practice you'll have to try hard to detect a difference. At longer focal lengths, the f/3.5 version looks to be taking the lead though.
Only if you plan to do astro photography, you might want to opt for the faster version, but I guess there's better lenses for that, like the Tokina 11-16 or the Samyang 14mm.
Between the Sigma 10-20's I'd go for the f/4-5.6 version.