The one thing that makes the 5D III stellar for shooting events / weddings / reportage i.e. "people in action" stuff, is not just its AF system, but the controls associated to it, and especially the following things :
- The ability to register an AF point (that includes the automatic selection mode), and then bring it up with the AF-on, exposure lock of DOF buttons.
- The ability to go from One shot to AI servo with the DOF preview button
- Custom modes.
Just as an illustration :
In my C3 mode, I use 9 points extended af mode when pressing the shutter button, but automatic selection when pressing the AF-on button. At anytime, I can switch between One shot or AI servo if the subject starts to move, either in manual point selection or automatic selection. The exposure lock button is used as AF stop (if an object blocks the subject view for example). So it's like having two AF point selection modes quickly available, either in One shot or AI servo modes.
In my C1 mode, instead of switching between One shot and AI servo, the DOF preview button serves as a second registered AF mode, so it's like I'm having three AF point selection mode quickly available at the same time : spot AF, extended AF, automatic selection AF.
This is massively powerful for shooting living things, which tend to be, by nature, quite unpredictable subjects. Since I see you're shooting events and weddings, that could be very beneficial.
You'll also benefit from having a second card slot, although unfortunately the SD card slot doesn't support fast cards (why Canon ? WHY ?).
On the other hand, from the files I've been playing with in Capture One, I find the 6D sensor slightly superior at higher ISOs, and at least as good at low ISOs as the 1DX, that is to say, again, superior to the 5DIII.