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.
DSLR
With mirror
The mirror is in front of the sensor and it is used to reflect the light, coming from the lens, into the viewfinder, so you can use your camera without using an LCD, just using the viewfinder can save lots of energy and your camera's battery will last much longer.
More ergonomic
They feel good on your hand, I can only compare my DSLR Canon 200D with my wife mirrorless Sony A6000 and the bigger size of the DSLR make a really big difference, whenever I grab the mirrorless I always feel it can drop if I don't take enough attention on where I put the grip but with the DSLR it's just so simple that I don't really need to think about it, I can feel the camera fitting perfectly in my hand, even grabbing it with only my fingers is enough. Also is easier for me to change settings when I have full grip on the camera.
Same quality but cheaper
It seems to me that if you want the same quality in a mirrorless camera you have to pay much more than a SLR. It's probably due to the reduced size that make the all hardware a little more expensive to make.
They can be heavy
I like to feel some weight on my hands, I feel I can stabilize the video better, even the movements can be smoother but this is really something you should try by yourself.
Mirrorless
No mirror
This bring one advantage and one disadvantage, you can shoot much more photos in one seconds compared to a DSLR of the same price, since they don't have a mirror that have to be moved away from the sensor every time you take a photo. They consume more battery, the only way to check what you are shooting at is looking through an LCD, that can be the main one or a small LCD located inside the viewfinder if the camera have one.
More expensive
As I said for the DSLR, probably due to their small size the all hardware is just more expensive to build.
Smaller
You can put the camera in a daily bag without using too much space, no need for a camera bag, also you might be more comfortable shooting in crowded places since people might be less scared of you.
Lighter
You can use the neck strap without feeling the camera is taking off your neck.
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.