The quality also depends on your skill level with the converter, and getting to know its personality. In my experience, the Nikon software makes a better looking conversion with the default settings than ACR or C1pro. So if you only compare using default settings, you would likely choose the manufacturers converter.
One advantage to using converters like ACR, Lightroom, or C1 pro is that you can learn one converter very well and use it with many different cameras.
The qualitative differences span many areas as well. Aside from the color reproduction, there are differences in sharpening, noise reduction, highlight recovery......
You may also find that one converter's default is better for garden photography, while another is better for skin tones.
This decision is really no different than shooting transparency film. Every lab in town has a different look in their processing. One made Provia look better. The other made Astia look better. One had a 2 hour turnaround, the other... 3 hours. One charged more for a rush. One had a pickup service. One lab ran 1/3 stop brighter than the other.
In this aspect, digital isn't really different than film, except that you can run your one piece of film at every lab in town over and over again (and you don't have to pay any messenger fees).