Here is the PNG file and what it looks like in a QWebView when accessed via http://sstatic.net/so/img/logo.png:
When accessed via HTTP:

<img src="http://sstatic.net/so/img/logo.png" width='250' height='61' />
When accessed via a resource:
http://files.quickmediasolutions.com/qt_res.png
<img src="qrc:/images/logo.png" width='250' height='61' />
As you can see, the only modification was the src attribute of the image tag… why the drop in quality?
Edit: The file is being shrunk via width: and height: in the style attribute, if that makes a difference. I updated the code.
The 2nd image is being resized from 300×83 to 250×61. The original image is anti-aliased, the anti-aliasing pixels are getting lost in the resizing operation. That affects the perceived image quality badly. This image will only look good if it is shown with its original size. An image editor that uses a high-quality bi-cubic filter might do a better job, not so sure.