The DA15mm is not as wide as the 10-20, obviously. It's also not really any sharper. It is legendary for flare resistance. If you like the sun in the frame, that is an addictive lens. We have a huge thread full of examples from this lens. here:
The 15mm Limited controls my mind - club - PentaxForums.com
It's not a "technically great" lens. The corners are a bit soft until f8, but there is really something about it. When I take out the 15, my shots are just better.
You can get the Sigma 10-20 in either version, I also have the Sigma 8-16 which is sometimes available, though not super common. The Tamron 10-24 is also available, though the comparison tests show that lens is not quite as good as the other choices, it's a great value and still a decent lens.
As suggested, the 10-17 fisheye is another choice. Not super fishy at the 17mm end, and still very very wide at that end. The 10mm end has a 180° view. Amazing.