I've been testing a refurb 6d for a week now. The AF is abominable. AF misses plenty. This is both after focal calibration - twice - and tuning by hand.
With my f2.8 lens the 6D center af is not great because it sometimes misses, but certainly not that bad - I'd say the real failure rate is 1 in 25-50 shots. Otherwise the center af point is more precise than my 60D in stills shooting, so I'd say there's really something amiss with your copy.
Lastly, I'm pretty disappointed at the 6ds sharpness. Images - when accurate- are pretty soft out of camera. Not one image has any of the clarity from my t2i files. I'm not so sure it's the AF entirely, as I've been viewing raw files from around the net and they all show the same soft, oily looking effects.
In this case it isn't your af. First off, the 6d is tuned for high iso so files at low iso are somewhat less sharp than 5d3 which itself is less sharp than 5d2 - but to a degree that shouldn't matter much in real life shooting.
What you a experiencing is the "ff look" which can be a bit irritating when coming from crop - also the lenses look completely different on ff vs. crop (shallower dof, different bokeh and sharpness). The noisier crop images can be indeed be perceived as "crisp" was also my very first reaction with my new 6d - I got used to it and now use my 60d for macro where the "crop look" seems to be better, next to the deeper depth of field.
Last not least ff raw files need more postprocessing than crop, they look flat and blurrier than crop - this changes even after a very small degree of tuning, but if you're the sooc type this might be disappointing, in this case get a 70d and better lenses.