At the same shutter speed, the same sized print (or downsize of a bigger image) would NOT be different no matter the density (22MP vs 36MP).
True, in order to benefit even more from a higher density sensor, it is advisable to use higher shutter speeds in such fast action situations.
Again, a 36MP sensor is no worse recording image than a 22MP at the same shutter speed, it can only be better.
Here's a scenario for you that think they're equal in noise. When you increase pixels you also need to shorten your shutter speed to not show motion blur. I tried the D800 and I had to have at least 1/2500s to freeze a bike messenger I tried outside the shop where I work, that means going to 3200 iso whereas with the 5d3 I had iso 1250 and around 1/1000s, no motion blur on either, but I was over a full stop higher in iso , making the image, of course, more noisy and less DR (that some of you are EXTREMELY conserned about).
Not worse, it just shows the motion blur more than lower res. And if you crop, which I assume is one of two reasons why people want 36 mp, you still can see it better, that's a fact.
Zoom them both in to 100% crop at the same settings and it becomes obvious. It's not that 36 mp is more prone to motion blur, it's just that the higher level of detail reveals it.
And to say the 36 image is no worse than 22 at 22 is a pointless point, why would you buy a 36 to use it at 22?
Normalize res and all this, what a waste.
"oh look, the 5d3 is no better at focusing than the 5d2 when I use an f5,6 lens and aim at a completely white surface, man, Canon has failed and left it all in the hands of nikon"