The conventional distinction between qualitative and quantitative research has always been misleading: a kind of hangover from Research Methods 101. So, asking the question about one vs the other in a binary way is not helpful. Try something a bit more nuanced.
Quantitative data can tell us what happened. Qualitative data helps us understand WHY it happened. When it comes to social situations and the media, I think that understanding the WHY of the dynamic is important.