This is like the difference between veal and beef. The younger animal has softer meat and a different kind of fat.
Honestly? I don't exactly understand why but the intuitive explanation is that animals that are allowed to roam and browse free are ... more healthy?
Comparing free range animals with cage grown ones, the most obvious difference is going to be muscle development: animals that grow up in cages will never have much muscle mass, since they simply have no way to exercise - they will have weaker muscles, and this will be detectable as a different taste and texture. Similarly, fat deposits will often be in different places and of slightly different kinds for animals that can exercise vs those that can't.
Additionally, cage grown animals are typically also fed a cheaper diet, and the diet will always have an impact on the taste of the meat.
And yes, the cage grown animals will likely also have different health issues because of the lack of exercise and poor diet, that free range animals won't develop. But I believe the other factors will have a much bigger impact, especially since these animals are typically harvested while they are pretty young, and may not have developed too serious conditions.
Growth hormomes.
As an example, I've seen some US chickens as large as Canadian turkeys...
So free range, may not be getting growth hormones in the feed...
See, eg, https://ask.usda.gov/s/article/Are-hormones-used-for-livesto...: “No steroid hormones are approved for use in poultry”
It’s certainly true that today’s meat birds are MUCH bigger than heritage breeds, but that’s a result of selective breeding, not hormones.
The size difference is stark, so I still wonder re: selective breeding.
“ Most broilers find walking painful, as indicated by studies using analgesic and anti-inflammatory drugs. In one experiment, healthy birds took 11 seconds to negotiate an obstacle course, whereas lame birds took 34 seconds. After the birds had been treated with carprofen, there was no effect on the speed of the healthy birds, however, the lame birds now took only 18 seconds to negotiate the course, indicating that the pain of lameness is relieved by the drug.”