I can definitely see the red tones on the 5d3 in your hair in the first sample, but I have to say that I find the 5d3's grass sample to look far better on my calibrated IPS monitor. The red of the ball is far better and the photo looks to have more dynamic range. I can see the green is much more saturated, but it also looks far more neutral than the 5d2's shot, which looks to be white balanced a little toward the yellows... which is obviously more pleasing to most people, but isn't the neutral it should be.
I'm not sure color can be questioned this specifically right now... Lightroom's support for the 5d3 isn't even officially released. Quick question though... are you using Lightroom's camera profiles for your pictures or the generic Adobe profile? Because this makes a HUGE difference in color.