I was looking at what advantages has a DSLR compared to a mirrorless camera and I can tell you that there are not many actually, choosing one or another is not really related to the final quality of the photo or video, here I want to list some of the notable characteristics that I think should be considered when choosing one or another.
What about the quality
Not much to say about it, they are simply equal in quality, it all depends on sensor size, lens quality, and by how bigger is your wallet.
So what camera should I buy?
First I would look at these characteristics I listed here in order to decide if a DSLR is better for me instead of a mirrorless, and only then I would look for quality spec, so I would look for sensor size, image resolution, video resolution, frames rate and video compression during recording. Another characteristic I like to check is how good colors are matched to the real ones, and this depends on how good the sensor behave on catch the light and converting it in real colors.