I only allow with shell when it's raw quail eggs because my lot enjoy smashing them open, so it's mostly just for a bit of enrichment experience. I only do raw eggs for our ferrets, cooked foods have most of their nutritional value lost from being cooked as compared to when they are given raw.
It's always best if you can give the egg with white and yolk whipped together/scrambled with a fork. I've found room temperature eggs have the white less gloopy and allow it to mix together easier. Though I still have one who doesn't like the whole mixed egg and will only eat yolks, so he gets just the yolk for him. The white should just never be given by itself, as over time it can lead to a biotin deficiency.