I definitely think you can tell if the fish are happy/feel safe. At the moment I am experiencing this myself - my fish lived in a heavily planted 60L and they didn't swim about much any more, I can't describe it but I got a feeling that they were not enjoying their home. They were a bit more happy and active when I put lots of dead leaves in the tank though, I knew that the tank space wasn't enough and I thought the environment wasn't varied enough to keep them satisfied. This unnamed discontent is why I got my 180L, to try to make them happier. I also spent a lot of time watching videos of fish in nature and saw a big difference there.
Flash forward to now where they live in the 180L, which I scaped so they would have every aspect of their needs taken care of - sand for sand sifters, lots of different holes and caves, a variety of dried leaves in piles and driftwood, thick vegetation with lots of moss, a good expanse of clear water to swim freely in that was protected at the sides, some heavy shadows to feel safe in. I have immediately noticed a difference. I see all of the fish far more, they are more active and they all really use the space. They hunt and forage constantly, and the tetras swim about constantly and create different formations and groups. The apistos, which to me seemed to be the happiest fish before, have started to hunt which is a new behaviour to me, and the kuhli loaches at night swim around the whole tank draping themselves on leaves in a group. To me they just seem to feel more safe and act "freer".
I feel a noticable sense of relaxation and calm, where things felt more tense before. It's just a feeling really but I do feel that it has improved things. I especially get this feeling when I "spy" on them at night when they think I'm not around and can't be seen at all, all the fish are out and about in a flurry of activity, whereas in the 60L even at night there wasn't much going on. The tank is now so much more enjoyable to watch as well, seeing the fish like this is a relaxing experience where I don't need to worry any more.
I think you can really tell this in the shops too, you can see which fish feel unsafe, stressed or depressed, and which are quite comfortable and confident.