Well, as Ziser said, f/4 or f/5.6 would be better since it gets more of your subject(s) in focus, and with a strobe you get plenty of light while stopping down further would make it harder to get any of your background in the image, it'd end up basically just being extremely sharp, or you'd see drastically more shadows from the strobe.
The thing to know about the 6D, is it's not really considered a 'professional' camera as such. Sure, it's a fine camera, but features and build quality is generally not up to 'pro'. Heck, Canon only calls the 1D-series as 'pro' cameras, everything else isn't.
When you say 1 stop better, are you just talking about sensor noise performance or AF sensor performance? Even though the center point AF sensor works fine with f/4 lenses, I believe it also has a double cross-point sensors there which are likely only available on an f/2.8 lens. Thus, you still get the point where your AF will likely be improved by having an f/2.8 lens, even if you take the shot at f/4 or f/5.6, even in available light.
The other factor is, if you could choose between f/2.8 or f/4, and the difference was ISO 3200 vs ISO 6400, which would you chose? If ISO 6400 is perfectly fine with you, go for it. If you want to drop down to ISO 3200, or increase your shutter speed while staying at ISO 6400, then you'd need to go for the f/2.8 lens.
There is also another thing that you may not think of, is that lenses wide open generally don't perform their best. I'm referring to resolution, CA, etc. f/2.8->f/4 can often make a difference for a lens, and f/2.8->f/5.6 can make a big difference. That's why the top end primes go to f/1.2-f/1.4. Sure, being able to shoot wide-open and get pretty good performance is great, but if you stop them down to f/2 or f/2.8, you get some really great performance while still being able to keep higher shutter speeds.