I too have read that the bigger lenses do AF a little quicker on the 1 series bodies because of more battery power. The reported reason is that the motor can move the big glass elements faster with more battery power. I think the 1DX and 1DMKIV batteries may actually have more current output in terms of mA not necessarily voltage. I am not certain but it seems that is what I have read. AF speed depends on many variables so it might be tough to tell the difference in a typical situation in the field.