I have been doing video as a sideline for about 12 years now. While photography background certainly helps in many ways (understanding most of the technology, framing, exposure etc), the big difference is continuity, movement, timing and rhythm, which all need either preplanning or just having the "touch". Also shooting video is not an instantaneous affair, but getting the shot often means you need to be consistent with your choices, you can not change your viewpoint or framing suddenly, and need to stay ahead of what is happening even more than with stills. Audio is often the big problem, getting truly good audio often requires more work and investment than getting the picture. Just plugging a shotgun microphone on the hotshot is NOT going to cut it in the long run.
At the moment I like to use a real video camera whenever I can, because it is much more flexible and ergonomic than a stills/video camera, with working auto almost everything when needed, and 20x zoom plus 2 channels of professional quality audio inputs with phantom powering for the microphones. The camera is Canon XH-A1, a fairly big one by modern standards. On the audio side I have a pair of Sennheiser radio lavalieres, pair of DPA 4060 lavalieres (cable or radio, cable is always better if it is possible to use it that way), mono & stereo short shotguns from Sanken, Rode and Pearl, Sound Devices 722 stereo recorder, Sound Devices 302 field mixer, couple of Rycote Zeppelins for outdoor use, etc etc. Plus loads of other more expensive stuff for classical recording, done as a hobby.
I try my outmost to avoid having to do both video and stills for the same project. Both suffer if I must do both. With something staged it is ok, but for reportage or news it is almost impossible.