There's no nutritional difference between brown and white eggs

Exactly something that the white egg-faction of Big Egg cartel would pay you to say.

Dagnammit - they're onto us and our misinformation campaign.

Best get back to just painting them brown.

But brown does usually mean "biggest egg you're going to get here"!

Yep brown eggs are laid by brown/red coloured breeds which do tend to be larger than white hens. They have the same nutritional profile though.