I have both and love them both.
On the Sigma 10-20 there is no manual focus switch so you have to switch to manual focus via the menu on the D3200 if you want to focus manually due to low light.
Check out my london night time photography, a lot of that was done with the 10-20mm
I switched from the 18-55 kit lens to the 17-70 and love it. At the same ISO, aperture and focal length the 17-70 was noticibly sharper. Opening up to f/2.8 is extremely useful and this is my normal lens and it is nearly always on the camera unless i need the reach. The 17-70mm is about twice the size of the 18-55mm and probably over double the weight.
With the 10-20, it is a great lens, you can get some great photos, but you need to work harder. Taking a photo standing up will generally be boring as everything will seem to be miles away. I find being low (open the tripod legs to the wide setting and use the short pole on my red snapper tripod) really helps to give you some foreground detail.
I will be uploading some more photos this week on to Flickr, so keep an eye out.
My favourite picture is the wooden pier which has been my desktop background for over a year now. This was take with the 10-20mm, ISO 100, 30 second exposure at around midnight in October. I was lying on the floor on the banks of the Thams and a number of people asked me if I was OK.
The lit up trees was directly behind me, was also taken with the lens, as was the church and city hall.
It is my favourite lens of all, but I don't always use it. You have to think to use it.