I shot the DA l 18-55 as a "Single In" lens -
Here
and I have shot the DA 15 Lts as a "Single In" lens -
Here I know many others of our "Single In" participants have shot both, so you might want to hit that group and see what there is to be seen.
The DA 15 is much smaller, it has a built in hood. It has a 49mm filter thread so the filters one might want to use might be less expensive. The build quality is excellent. And finally the 15mm fov is much wider than 18mm (21mm on FF versus 28).
The DA L 18-55 is a fine lens, and if you are trying to stave off LBA or GAS... I'd stick with it. Besides the plastic mount - it is a nice light versatile lens, and when used with good technique gives excellent results. Most who complain of softness are shooting at low Shutter speeds where Higher ISO or Flash would benefit.
If you already have the kit lens and are considering acquiring another lens, you might look at and ultra wide zoom... as the DA 12-24 (
here when I first got started with Single In and more recently
here)or Sigma 10-20 is that much wider than even the 15mm. (Just to throw a wrench in your question)