Have a look at the other side of the tank. It's empty. The fish are doing what fish do, they swarm to wherever the food is. For all I know, they may be no more crowded than the fish in a regular aquarium in someone's house.
That's not a great comparison tbh. Who's to say that keeping fish in an aquarium isn't also cruel.
There are ways to measure these things, primarily by measuring the levels of stress hormones, which are known to operate in a very similar way among fish and other animals. This paper outlines one proposed way to do this.
Stress Response System in the Fish Skin—Welfare Measures Revisited
Without having seen the results (appears there aren't many yet), my bet would be that when these tests are carried out, they will find significantly raised levels of stress hormones in farmed fish.
The overall health of the fish as indicated by the quality of the meat is also relevant. Again, work wrt distress seems pretty provisional on this. It's only surprisingly recently that it's become widely accepted that fish even have the ability to suffer. Then there is the fact that the meat itself is generally fattier and less nutritious than wild-caught fish, which is another indicator of a life not-so-well-lived. (I'm using the word meat to include fish here - I don't see any good reason not to place all animal flesh in the same category, in fact I see only good reasons to use just one category.)
Farmed fish welfare: stress, post-mortem muscle metabolism, and stress-related meat quality changes
comparison of farmed vs wild caught salmon nutrition-wise:
Wild vs Farmed Salmon: Which Type of Salmon Is Healthier?
This is a pity for me. I wish the evidence pointed a different way, but I can't see fish farms as anything other than a non-starter in terms of animal welfare. Sustainable levels of wild-caught fishing are much more humane, imo - just being one of the many predators most of these fish have. But there of course the operative word is 'sustainable'.
And that's before addressing the issue of the input of feed into the fish farms, or issues to do with diseases and how these not only infect the farmed fish but also leak into the wider ocean ecosystem. Some things, like oysters or mussels, ok, they're creatures that don't move around anyway. But free-swimming fish in a watery cage? That's factory farming really, isn't it, with all the accompanying issues to do with health, welfare and sustainability.