I realised I had two boxes of eggs bought from the same farm shop a week apart so I decided to do a bit of an experiment. I think we can assume the eggs are roughly the same size and have come from similar chickens fed the same feed.
I poached them both in the same pan, with clean water for each. The pan was left to heat for the same time on the ring so it was approximately the same temperature. The eggs were poached for the same time. I used the 'vortex' method with nothing added to the water .
The fresher egg came out if anything slightly underdone, with a bit of the white still slightly 'runny' . The older egg came out overdone - the yolk was more or less completely set. Also the newer egg looked much better; the white had a folded look and it was more spherical. Whereas the older egg's white had set very uniformly and it was very flat - in fact it looked like a well cooked fried egg more than a poached one.
Nevertheless both were very tasty

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The conclusion I would come to is if you're going for presentation, get a fresh egg. If you're just looking for something to have on toast of a Sunday morning, an older egg will do just fine as long as you keep an eye on it when cooking.
Jon