What does DOF have to do with low light sensitivity?
For me I know that my "working" DOF with my GH4 requires me to shoot at f/2.0 - f/4.0, so switching to a FF camera would mean shooting at f/4.0 - f/8.0 to get the same "working" DOF that I am used to.
Sure you can shoot at wider apertures but will you get the shot you are after ?
I remember watching all these terrible videos when the Canon 5D Mk2 first came on the market because so many people were shooting almost wide open and it felt like my eyes had gone myopic because the DOF was paper thin and virtually nothing was in focus.