A lot of time the difference is the age of the flower. Some fade faster than others. Color register is another problem. Plants with a blue tint such as lavenders and bluish mauves do not photograph well. Peonies do have different flowers on the same plant. If you have one that makes a main bud with side buds the side buds do not match the main bud by the time they open.

Check out Carsten's website for differences in different peonies.

Here is a link that might be useful: Carsten Burkhart

I agree with maifleur and only want to add that in your sample one picture is in full sun while the other is in the shade. I try not to take pictures of flowers in cases where the camera uses its flash, as it washes out the color. Al

I think the difference is not that huge, these two picture is from different angel, as for the color, you might notice the color setting or balance of the camera.