Cats are happy when they are in a safe and comfortable environment. This is why it is so important to ensure your cat run is set up with vertical climbing space and places to hide, as well scratchers and toys for stimulation.
If you have an indoor cat and are considering moving it into an outdoor cat run, introduce it slowly to the new outdoor environment. Limit its time outdoors and be sure to remain with the cat in the beginning. Gradually extend the time your cat is left outside on its own until it has adjusted to its new outdoor environment.