For example this study (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9658713) mentions that "Providing pasture to hens yields egg yolks with a lower omega-6:omega-3 (n-6:n-3) ratio and significantly greater vitamin A, vitamin E, and carotenoid content compared to egg yolks from caged hens".
Also the colour of the yolk is a lot darker - more orange than yellow - and it has better structure - doesn't break so easily when ie baking. And of course the taste is better but then we come back to the subjective part again :)
Essentially all commercially farmed eggs are from caged hens, unless either you live in an area where caging hens is illegal, or the eggs are explicitly advertised as being cage-free.
Furthermore, being cage-free is not sufficient to reap the benefits discussed above. "Cage-free" hens are generally still crowded so tightly that they do not move around much, and do not have access to the outdoors.
Pasture raised hens do have the benefits described above, and essentially no commercially farmed eggs are pasture raised except those specifically advertised as such.
> essentially no commercially farmed eggs are pasture raised except those specifically advertised as such.
This is a silly thing to say. Of course if a chicken is pasture raised it'll be advertised as such on the carton, those eggs go for 3x-4x as much per dozen!
chickens are omnivores and opportunistic predators. if they get to roam around and get bugs/worms/etc in their diet, that is actually reflected in the nutritional composition of the eggs and meat. there are a lot of high quality eggs for sale with much more nutritious yolks. more expensive of course.
free range chickens also get more sunshine and exercise, which reflects positively too.
I don’t dispute the “better” part because that is so subjective. But how do you know they are more nutritious?