The main difference in a mirrorless camera against a standard DSLR is that the mirrorless one is smaller with simpler construction. No mirror/prism - reduces the size, the light falls directly on the image sensor.
The AF speed was a drawback in the earlier versions of DSLM cameras - as they used contrast detection which was slower than the phase detection used in the DSLR. But the modern range of DSLMs have overcome this issue and uses hybrid phase/contrast detection and it is no longer a problem.
Video quality of the DSLM is supposedly better and if you can afford a DSLM is a good choice.