Personally, I can't tell the difference in flavour between a fresh egg and an old egg. Texture is the only thing I've noticed. Though, for instance, that can be quite important in some egg dishes like tamagoyaki. For flavour, a much bigger difference can be seen from the diet of the hen. Grain fed battery hens have pretty bland eggs. I obsess about my tamagoyaki, so I'm willing to go to some extremes to get good, fresh eggs.

If you know anyone with chickens, get an egg off them. The difference between the eggs and store bought, free range, is night and day. I don't know why, but the yolk is orange for starters. It may have been due to the species of chicken I suppose?

It's to do with diet. IIRC, some farmers feed their flock flax in order to get more orange yolks. But free range hens that have access to insects tend to have a nicer flavour in my experience. Generally speaking, an egg with a hard shell and a very bright yolk will be nicer and that tends to correspond with free range hens. But, climate where you live will influence how realistic that is.

If you're lucky, your friend with chickens might have blue-green egg shells.

You can buy eggs with blue shells and bright orange yolks in UK supermarkets, I ate some yesterday.