I wouldn't get a zoom lens with anything greater then 3x optical zoom. but if you are looking for 1 lens fits all, why did you get a dSLR? This in no way, is a personal attack.. it's just a matter of trying to understand the reason for jumping into a dSLR where as you are familiar with what the S3 IS can do.
But to answer your question, between the two, i would get the Sigma... If i have a third canon choice.. i would. but with 10x optical zoom.. you are going to lose some quality in the glass itself.
If I were to look for a walk around lens.... i would look at getting the 17-85 F4 - 5.6 IS. or.. i would first use your kit lens... take it out one day, and shoot what you normally shoot. then you can see if you need more on the short end, or you need more on the long end. That will help you decide on a better lens solution then a 1 lens fits all kinda deal.
you will learn to LOVE IS... especially on the long end. You will not appreciate how much the IS adds until you don't have IS.
Would not be able to take that hand held without IS.