As someone who primarily works with video, I was extremely impressed with the quality of video that I would see coming from the Canon EOS 5D Mark III. Eventually, I had the opportunity to use one and I wasn’t disappointed.
The 5D, unlike the 60D, contains a full frame sensor and uses only EF lenses (not EF-S). If you are upgrading from a 60D or other “cropped” sensor model, you may have to invest in new lenses as well.
The Canon 5D Mark III is still available for purchase, but the newer 5D Mark IV has replaced it in the line. I have not personally used the newer model, but I am confident it will deliver the same quality.