I am considering buying a Sigma 10-20 mm F3.5 wide angle lens for my canon 550D, but not sure what the benefit would be compared to using the wide angle end of my existing Sigma F3.5-6.3 18-250 mm lens?
You're comparing ultra-wide versus "simply-" wide. It's as if you'd compare a 200mm tele to a 600mm one.
Those 8mm do in fact have a great significance, for example:
I do think this illustration is a tad exaggerated, but you get the feeling.
The difference between 10mm and 18mm, especially on a crop sensor, is significant enough in order to justify the purchase if you really need the wide angle. (is like 16 mm vs 29 mm on Full Frame). You can see some field of view comparisons at different focal lengths here. In fact, if you pay attention almost 75% from Sigma's 10-20 range is uncovered by Sigma's superzoom. If this doesn't matter then why Sigma produce(d) such a lens? Also Canon has an 10-22mm offering which should give you a hint that we're speaking about different things here.
An 10-20 zoom is an entire different beast than 18-250. The strengths (read: image quality) in the "wide" area of the spectrum are quite different. For example, Sigma's 10-20 has less distortion at 12 mm than Sigma superzoom at 18 mm (!) while at 20 mm the 10-20 is (near to) distortion free (ok a small pincushion can be spotted) which leaves in the dust the pronounced barrel distortion of Sigma's superzoom. The phenomenon isn't (IMHO) very odd, taking in account that 18-200 has a much broader range to cover. Generally speaking, the image of IQ tends to increase when the zoom range decreases.
I'd add here the constant aperture which in low-light situations (for example indoors, twilights etc.) can be critical.