One similarity between qualitative and quantitative research is that raw data is ultimately qualitative. Even though numbers are unbiased, the researcher still has to choose some numbers and disregard others. So, while the numbers themselves are objective, the process of choosing them and justifying why they are more important than other numbers is qualitative, which makes all research qualitative to some degree.
While some qualitative data is simply a researcher's impressions, other qualitative data is "massaged" into quantitative data. Examples of this include surveys where people put their impression of something on a 1 to 5 scale; while the impressions are qualitative, they are expressed in a quantitative way. This allows researchers to turn qualitative impressions into quantitative data.
Both qualitative and quantitative research methods involve the researcher. The difference is in how involved he is. In a qualitative anthropological study, for example, the researcher may "embed" himself with a group of people and write his impressions. In a quantitative medical study, though, the researcher will devise the study on her own. Either way, the researcher is involved in a qualitative manner at some stage of the project. This is a key similarity between the two.
The reality of quantitative and qualitative research is that most studies are mixed. In order to get a full picture of a topic, a good researcher needs to use a combination of both raw data and individual impressions. This is the key similarity between qualitative and quantitative research -- they are both used in most academic studies.