With a good caregiver the answer is “indoor cats have a better quality of life,” hands down.
An outdoor cat has the benefit of entertaining themselves, they can engage in natural behaviors such as climbing, digging, hunting, and sunning. If they’re a social cat, they may enjoy the company of other neighborhood cats.
However, they would be exposed to more daily stress. Stress scurrying across the road with a car barreling down, stress from trying to keep other cats off their turf, stress from coming across native predators or dogs.
It’s also more difficult to monitor health of an outdoor cat, so although they may enjoy hunting and digging they won’t enjoy having worms. They won’t enjoy struggling to pee, or being constipated, which their owner may not pick up on because they do most of their business in the neighbors garden.
Their deaths are often less “quality” as well, the reason free-roaming cats tend to live shorter lifespans is because of trauma and illness. They may enjoy sunning themselves, but wouldn’t enjoy dragging themselves to the side of the road to die because they chose the wrong patch of asphalt. They may enjoy climbing, but wouldn’t enjoy it if a bird of prey snatches them off a branch.
Indoor cats with inadequate owners will become bored, depressed, and often destructive. If fed poorly they’re more likely to be obese or develop health issues such as renal, thyroid, or urinary problems. This is, clearly, not a good quality of life.
However this can easily be remedied by providing an enriching environment using cat shelves, crinkle tunnels, cat trees, scratching posts, etc. and engaging in daily interactive enrichment.
If the cat craves the authenticity of an outdoor experience enclosures can be purchased or made, or they can be harness trained to safely enable their desire to roam. Ways to bring authentic outdoor fun inside is providing f/t feeder chicks or rodents, letting them hunt purchased feeder insects, or providing a dig box with soil from the yard if it’s pesticide free.
It’s also easier to monitor a cats health. Cats tend to hide if they’re ill, being around them all the time gives you a better feel for their behavior and if somethings off. It’s also easier to monitor their litter use and urine / stool health, which is often an early warning sign. Being able to notice the issue sooner means less time the cat is suffering, and if it’s a serious health issue the cat then has a better chance of recovery.
The quality of death is often better, a well-cared for indoor cat is most probably going to die of age or from euthanasia.
So the quality of life for an outdoor cat may be situationally better than the quality of life of an indoor cat who has a unqualified owner, but an indoor cat with an owner who knows what they’re doing and is willing to put the time and effort into having a pet isn’t missing any of the “pros” an outdoor cat experiences but is spared the “cons” both the outdoor cat and the poorly owned indoor cat suffer.
If quality is the deciding factor for I would suggest looking through this testimony from behaviorists, veterinarians, and other experts who encourage indoor cats and reading the part of the FAQ discussing the Indoor Cats Are Depressed myth.