This is a very complex question because there are many, many online qualitative research methods and many, many combinations of research objectives. And this doesn't even begin to address the definition of "quality." Since there is no easy answer I'll just toss in my 2 cents on a couple of items:
There is no doubt that the "data" from viewing people as they talk is largely missing from most online qualitative research methods. Viewing participants in person can reveal powerful insights, and the experience is insightful and memorable for the client viewer as well. This deficit is being overcome by online research software but, frankly, it is still a downside to online. So, when a direct comparison is made using this criteria, online qualitative research often comes up short.
On the other hand, online offers many opportunities that F2F does not. I love the opportunity to do longitudinal qualitative that several online methods facilitate (e.g., bulletin board focus group). Longitudinal studies are very difficult and very expensive F2F. Online provides greater opportunity to go into the lives of a participant for a 360 degree view of their interaction with a product or service. Online also gives us tools that allow people to be totally open with anonymity. There are other advantages, but you get the idea.
So, at the end of the day, the question to me is not which is higher quality, but which methodology best fits my needs?

