Don't forget that there is a considerable elevation difference between the south rim (6800') and the north rim (8000'). That 1200' difference makes a big difference in the weather.
If you are going to the south rim, October will be better. The weather will be cool, while the north rim could be covered in snow. Most of the facilities at the north rim close Oct. 15.
In August, the heat at the south rim will be nasty, while the temperatures at the south rim should be quite nice.
Retired electronics engineer. Avid paddler & birder.
2011 Silverado 2500HD, diesel, 4x4,crew cab, 8' bed
Palomino Puma 253FBS (27' 5er) & '94 19' Class B