Since you already have Canon system, 6D is your best bet. I had OMD EM5 before and i can tell you this right now, camera is nice but it has limitations. Light weight and good to excellent image quality (depends on the lens). I had the best lenses they have to offer, the highly praised 75/1.8, 45/1.8, Panasonic 25/1.4 and the widest zoom 7-14. They are capable for any photography task, but it's more suited for travel or street photography. If you do serious gigs, like wedding, studio portrait, it's not up there yet compare with real DSLR like Canon...Show more →
For the OP who wants it as a family camera, I think it is ideal...more so than a DSLR as it will be taken with the family on all outings whereas a DSLR will most likely be sitting on the shelf on most outings. At least that is my experience.
I have both a DSLR system and a Fuji X100. My Fuji goes with me everywhere so I get photos I normally never would. However if an outing is specific to photography, my 5d2 camera with an assortment of lens comes along.
For general family pics, the OMD is an ideal setup.