I used both lenses before, and I would go with 12-24.
Actually there is not much difference to talk about. But the 12-24 wins with constant F4. On UWA lenses, there is not much bokeh to talk about and the F4 gives pretty good sharpness and large DoF already.
Whereas the 10-20 lacks sharpness until I reach F8 or smaller. Throughout the zoom range, 18mm is the sharpest.
Both lenses offer low distortion, I mean barrel and pincushion. As for rectilinear, you can't avoid it, and so I prefer to have 12-24 to 'prevent' me from getting too much rectilinear distortion in my shots.
Another way is to keep subjects at the centre of the frame, where distortion is least. However this is not a practical method if you're doing full body shots. So again, the lens with least distortion, 12-24 wins.
I don't mind taking a few step back to change my perspective.