I have a 70-300 DO and am very, very pleased with it. Sharpness, saturation, and contrast at 300mm are very close to what I get from my 300mm f/4L prime. There is noticeably more optical distortion than the prime, and field of view at less than infinity focus isn't as tight, but those are to be expected from any zoom.
One of the things I had to learn, though, is to NOT use a UV filter with it. For whatever reason the UV filter with a DO optic seems to reduce contrast and saturation quite a lot. I keep a Canon UV filter on all of my other lenses for protection, but not the DO.
All of that said, though, the 70-200 f/4 L is a better quality lens if you don't need reach to 300mm, need one more stop of aperture, don't mind the white color, can't afford the DO lens, or any combination of the above. The IS version of the 70-200 is probably nearly as good as the non-IS (if past relative performance of Canon's IS upgrades is a guide). I bought the 70-300 DO for convenience and inconspicuity, but am surprised and continuously impressed by it's image quality.
For example, at 70mm and 100mm the 70-300 DO is better than the 24-105 L. If I want absolutely the best image quality and have the time, then I use the 85 f/1.8, 100 f/2.8 macro, 135 f/2 L, 200 f/2.8 L, or 300 f/4 L.