Buy the Sigma.
This test has been rather more exhaustive/exhausting than usual, exploring many (not all) aspects of this group's behaviour, but the bottom line is that the Sigma is uncommonly well behaved for such a wide lens. To recap: it has no geometric distortion at 12mm, 14mm, 18mm or even 20mm. It has no chromatic aberrations. And it's fairly sharp. Oh, and it costs one third the price of the Canon.
To be fair, the Canon deserves to cost a shedload: it is fully 1.75 stops faster than the Sigma, it is compact and beautifully built, it has very well controlled distortion and it is sharp to the corners by f8. And you can't say that about many lenses wider than 24mm. Canon's wide lenses take a lot of flak, but this one is genuinely world class. I'm not saying that it wouldn't benefit from a bit of 'Digital Edition' trickery to keep the CA down, but on the whole it lives up to the expectations raised by the red ring on its rim.
The Nikon, however, is a stinker. As ever, it's always possible this sample isn't representative, but too many other reviewers have found the same problems with distortion for me to doubt these results too profoundly. Avoid.
Actually, given the problems I've had finding a 12-24mm worth keeping, the best advice I can offer is rather: buy LOTS of Sigmas; a good one is a gem, and accordingly worth hunting for.
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