Yup, both the same breed.
As far as I'm aware commercial hatcheries don't sell eggs, only hatched chicks.
Given it's, what, a billion dollar industry, if it hasn't been adopted as standard practise then it's easy to conclude it isn't a reliable method. When you consider that techniques like gene editing (among others) are being researched as a way to determine sex pre-hatch, and the costs and technology involved with doing so, there'd be no way they would be spending the money on research like that if there was a cheap and viable alternative. I can't believe the industry hasn't already tested morphometric egg sexing given how simple a concept it is.