The overall diameter of the 265/70R17 will be about a 1" larger over the 265/65R17.
That being said, going to the 265/70R17 will result in a 1/2" higher ride height.
I made this exact change in tire size a few months ago and am very satisfied with the results. The tire fills the wheel wells nicely, and there's less than 1" of clearance between the tire and the inner fender skirt when the wheels are turned.
Here's what my ride looks like with the 265/70R17's: