A current issue (which by all means for the likes of the photographer are benefits) with mirrorless systems is they don't appear as "professional" as an SLR does (small, lights, unoffensive or intrusive to the general public), it is unfortunate as, primarily the quality of the images are almost entirely down to the photographer, but also mirrorless systems can create equally beautiful images. An example is people want to see a bloke and his assistant turn up with 100 kilos of kit, 2 huge incredibly offensive camera bodies and lenses getting swapped out left right and center to feel they have paid their good money for a professional photographer. If you didn't know any better and you paid £1000 for a photographer at your wedding would you be impressed if he turned up with something marginally bigger than a point and shoot, a second prime lens and 40 spare battery packs? which brings me to my final points - the choice of propitiatory and 3rd party lenses is much smaller than that of the long established SLR systems, and due to the high demand of power for operation you get about 1/3rd the number of shots using a mirrorless system. This doesnt matter if you are a landscape photographer, but shooting sports or events where you are firing shots off all day you will need a good few spares.
For me, if you can only own a single system, I would go with a DSLR and wait 5 years for the technology to improve and the lenses more available - particularly second hand.
To answer the question after all that dross,
You can look through an SLR without draining the power
You can compose a shot in mostly darkness with much less trouble with a mirrorless
Autofocus is snappier on SLR's - currently
There is ZERO lag when looking through the viewfinder of an SLR
the resolution of the SLR viewfinder is infinite whereas mirrorless is as good as specified in the handbook.
The pros and cons of both are very much bone picking, they are almost equal in performance and give it a few more years I'm sure the decision should get easier.
I hope my post hasn't offended anyone
Cheers
Earl