Actually DSLR vs mirrorless got differences, and below are benefits of DSLR.
1. Sensor dynamic range.
2. Dedicated buttons.
3. Phase detection.
4. Better developed flash system, variety of lenses and accessories.
These are the reasons I still use mainly my DSLR for shooting fast pace events.
But then mirrorless nowadays are catching up. Even I am aiming E-M1.
Not true.
1) Sensor dynamic range depends on the sensor and many mirrorless interchangeable lens cameras are using the same sensor as their DSLR counterpart.
2) Dedicated buttons, mirrorless camera had as much dedicated buttons as DSLR, unless you are looking at smaller system like GM1, GF series, EPM2, etc. Look to GH4/ GH3, EM1, EM5, Sony's various mirrorless camera such as A6000, Fujifilm various cameras, NX1, NX30, etc, all these have as much dedicated buttons and dials as the DSLR.
3) Phase detection is getting more and more redundant, the Sony, Olympus and Panasonic all feature focusing as quick or in some cases, quicker than traditional phase detection AF speed. And they are equally accurate.
4) As for flash system... again not too accurate. Some of the mirrorless camera could use their extensive DSLR flash system too... like Olympus and Panasonic mirrorless system can use older Olympus DSLR flashes. As for the lenses, Olympus and Panasonic had a wide range of lenses that are almost as extensive as Canon and Nikon. Sony had this capability too, plus with adapter, it could use Sony DSLR lenses with almost no lose in AF speed and accuracy.
All in all, the technical difference between mirrorless system and DSLR are getting lesser and lesser, it all boils down to the handling of the camera as perceived by individuals and in some cases, digital viewfinder vs optical viewfinders... which was argued till death between the two camps of people.
My take (as I used both Canon DSLR and Olympus mirrorless camera + using of Nikon DSLR and some Sony camera system), the digital viewfinder, no matter how quick it refreshes after each shot, still have a little bit of lag... not noticable by many people, but I do feel it... whether that is important of not, is up to oneself, for me, it is a non-issue, just a little bit difference.
As to which camera I like best, I owned the OM-D EM5 with battery grip that gave you a deeper grip, I find it good enough for holding for long period of time, but somehow I still like the beefier grip I get with my Canon 7D and my bro's Nikon D90 and D800E. I have handle the Sony A6000 before, the grip is also okay, but not as comfortable (in my opinion) as full fledge DSLR... in another word, I like the older A77 type of camera grip.
As to their image quality, all of them are excellent, I can't tell much differences... sure the Canon is lagging behind in term of dynamic range in base ISO for their APS-C sensor, but for my uses (and I can vote for many other people's uses) this differences are really not that significant... or Canon would already have close shop by now.
