Don't say there is a difference. Name them. I too have a degree in the humanities. That isn't an argument.
> While there are tons of people who use mixed methods, quantitative and qualitative work tend to be very different in focus and even how they are written.
What's your point? Quantitative and qualitative work occur in science and in the humanities. It's not exclusive to one or the other. The difference between the two is that one deals with natural law and the empirical testing of those laws. While humanities do not. They most deal with the philosophical and the human condition. Morality or the best form of government aren't scientific concerns because they aren't about the natural world and its laws. It's not empiricial testable unlike say the speed of light.
Political science is not a science because it doesn't deal with nature and empirical experiments. Machiavelli was not a scientist because political science isn't a science.
Due to the inherent impossibility of repeating experimental conditions exactly (or in some fields, at all), the social sciences will never join the hard sciences, but instead occupy terrain adjacent to both humanities (where their data is sourced from), and hard sciences (where techniques are sourced from, increasingly for the "computational"- prefixed subfields).