How to copy and paste KeyframeEase to another property

What is your workflow again? Rotation and Opacity have different values. Opacity goes from 0 to 100, and Rotation goes plus and minus just about as far as you want it to. The graph editor displays the total number of degrees. I tried manually entering 30,000,000 rotations, and it finally went off the graph editor's ability to display a curve. 

I'm not sure how you are copying easing, but if I set an opacity keyframe at zero on frame 1, then another at 100 on frame 30, then I adjust the curves in the Graph Editor, then copy both keyframes and paste them to Rotation, I get identical Value Graphs and even identical Speed Graphs.

If I set a keyframe for 0º in rotation at frame zero, then another for 110º at frame 30, adjust the curves, then copy and paste the Rotation keyframes to Opacity, I get completely different graphs because opacity can only go from zero to 100%. 

Your screenshots show completely different values for Rotation and Opacity, so my previous paragraph does not seem to apply to your workflow. 

Please clarify your workflow in detail. Maybe we can help you figure out why you are seeing what you are seeing.

Your curves look different. But do they look the same if you copy both the keyframe values and their easing?
With different values and times of the keyframes, it is hard to judge if the easing is the same.

To me your curves look like for opacity you have a keyframe at about 7f and 25f whereas for rotation you have keys at 0f and 25f, correct?
Also, on your rotation the first key has value 0 and the second one value 100, whereas on the opacity it is exactly the opposite.

If I only look at the easing, it looks like for both properties the value change starts rather abrubtly and stops very smoothly, so it could be that you copied the easing successfully.