Hard to say, they both just kind of sit there...
How does one differentiate?
Darren's link does point out the possible differences that exist between the nutrition contained in each type of egg, but what you apparently really want to know is whether the differences are significant enough that you might want to switch to free range and pay their higher price.
These results add to the existing scientific evidence that the nutritional content of an egg is the same regardless of color or how the hens are raised. The notable exception is hens that are provided nutritionally-enhanced feed, which does result in higher concentrations of certain nutrients within the egg.
And here's that link: https://www.eggnutritioncenter.org/articles/are-free-range-eggs-more-nutritious/