Kirby, at the expense of stating the obvious, a picture made with a short focal length will "look" less sharp, all other things being equal, than one made with a longer lens. Being shorter, it will be wider, so the amount of details on the picture will be more, and each one will be proportionately less, if you see what I mean. I have used a 20mm pancake, and can testify to it being as sharp as you want. One thing you might look at is that I found that the Pana camera I used (in auto mode) nearly always selected f:1.7. If that is not the case with the zooms, then you end up comparing a short lens at f:1.7 with a longer one at, say, f:5.6, and the pancake won't look good by comparison. But, many times, sharpness issues have to do with user error. Too slow shutter speed, wrong AF point, all produce soft shots.
Hope this helps.