Manfred has given some very good advice here, and I only want to chip in with a few cents worth...
A DSLR camera was never made primarily for shooting motion pictures, and when doing so, it is no longer a DSLR. Functionally, it will behave like a camera without a look-through viewfinder. Generally, you should expect EVIL cameras to have better viewfinders for video work than DSLR cameras, and a mirror-free camera without viewfinder could be comparable to the DSLR in all functional respects.
The reasons for using still cameras in serious professional video shooting, primarily was that it was the cheapest large sensor cameras available, and that they offered some features at a very affordable price. It was not, and still is not, because they would be considered the best option for general video shooting. They aren't. They are an affordable means for professionals to achieve something that is unique, a very shallow depth of field, at a much lower price than comparable professional movie gear.
As Manfred has already pointed out, AF while shooting is a feature you would usually not want, and the same goes for auto exposure while shooting. Those are not suitable for video shooting, and serious video shooters handle those things manually.
What you would want for serious video work is override capability, so you can manually adjust whatever feature you like. A video camera should leave all possible manual options open. All still cameras that can shoot video don't do this, so you'll have to check thoroughly whether the camera you think might suit you really has the possibilities that you want. Those might include different frame rates, frame formats, fading possibilities, ability to use a faster shutter speed at any frame rate etc.
Many cameras lack several of the features you might need. There are cameras that don't let you choose manual settings when shooting video, and there are cameras that shoot only with very limited options regarding frame rates, shutter speed and ISO settings. So check carefully before you buy, that the camera you opt for really has what you need.