Many SLR owners have a range of specialized lenses for various situations. But it's also good to have a decent walk around lens, that is, a general purpose lens appropriate for carrying around as the only lens on the camera, usually for "snapshots" and other informal picture taking.
From their specs, both the Canon EF 28-135mm f/3.5-5.6 IS USM and Sigma 18-125mm f/3.5-5.6 DC appear to be good walk around lens candidates. They can zoom over a wide range, are small, and are reasonably priced. They also provide decent results, although as you might expect not the best results you can get.
Canon, which is about $100-$150 more expensive, has IS (image stabilization). This comes in handy in helping prevent camera shake at low shutter speeds. Sigma's advantage is the added coverage on the wide end: Especially on a 1.6x crop camera like the Canon EOS 20D, 18mm comes in very handy in trying to fit landscape, architecture, or group shots.
As far as photo quality, Canon has a slight edge in that it is a bit sharper and has less vignetting. The Canon and the Sigma have about the same amount of chromatic aberration.
The Canon is also ahead in operation: It is a Canon USM lens, allowing it to focus faster and more quietly than the Sigma. The Sigma is loud and slow. But one advantage the Sigma has is the "zoom lock" switch, which prevents zoom creep.
Size-wise the Sigma has the edge. It is designed exclusively for digital SLRs, which allows it to be more compact despite the higher zoom capability: It's lighter (13.5oz vs 18oz) and shorter when fully retracted (3" long vs 3.1").
Below are some comparison shots.
First, thumbnails (six at top from the Canon, six at bottom from the Sigma). These demonstrate at least three things:
The below shots, showing 100% crops from the edges of the fully zoomed pictures from above, compare the chromatic aberration. Both lenses seem to have about the same amount, although Canon features purple fringing, while Sigma red.
This last comparison shows the middle (just above the focus area) of the same photos. The Canon seems a bit sharper in these images. You can also see a slight but harmless yellow color cast in the Sigma pictures.
Overall summary? No slam-dunk here. Although the Canon has an edge over the Sigma with the slightly better photo quality and its wonderful image stabilization, Sigma is a decent enough lens with a hard-to-resist size and a reasonable price. But to me the more important edge the Sigma has is the 18mm wide end, and that is enough for me to consider the Sigma the more versatile "walk around" lens.