For recordings (or streaming) of over 29 minutes, a DSLR is not suitable. A DSLR will generally produce better image quality than a similar class mirrorless. However the max recording length of every DSLR is 29 minutes. The max recording length of every mirrorless except for the panasonic GH series is also 29minutes.
So the question becomes do you want to be able to change lenses, use a larger sensor on a modest budget or do you want the simplicity of a all-in-one solution?
I record events lasting up several hours. I simultaneously stream to multiple TVs while I record it to a SD card. I use a Panasonic GH3. This is limited to 1080p recordings. The newer GH4 and GH5 can do 4k but cost more and 4k files are a booger to work...