Depending on which of the two or three non-stabilized versions of the Sigma 70-200mm f/2.8 you have, I would be surprised if you gained much of anything at all by going to the Canon EF 70-200mm f/2.8 L IS. It is a 2001 design that is a very good lens for its time but is showing its age when compared to more recent offerings. You don't really gain anything from IS when shooting at or above 1/200 second if you are practicing good camera handling technique.

On the other hand, if you are considering the EF 70-200mm f/2.8 L IS II released in 2010, you will gain quite a bit in terms of optical performance with that lens compared to the non-stabilized Sigma 70-200 f/2.8 offerings. When released in 2010 it was considered the best zoom lens in the world (The more recent EF 24-70mm f/2.8 II now seems to get a nod as the "best" zoom lens). Unlike most zooms that have stronger and weaker focal length ranges, it performs well at all focal length and aperture combinations from 70mm to 200mm and from wide open at f/2.8 all the way to minimum aperture. In many cases it gets very close and sometimes equals the performance of many of Canon's prime lenses when shot at the same focal lengths and apertures.