Both Sides for Bells
In the twelve years that I've had my cat, Bells, he's experienced both lifestyles. To summarize, I feel he's healthier and happier with his outdoor time.
When we first adopted Bells, we lived in a suburban neighborhood. It was a new development and therefore not very populated for the first year or two. At first, we let him out in our backyard only under supervision. He started climbing fences and exploring, and eventually he spent about 50% of his time outdoors until about 11pm when he came in for the night.
His vaccines were always up to date, he had a collar and ID, and we took measures to prevent heartworm, fleas, and the like. He did get in a scrap or two, but he always came out with only a scratch.
Our family later relocated to an apartment in the city, and poor Bells's outdoor life came to an end. During this time he gained a lot of weight, presumably from his lack of exercise. (The weight gain was also partially our fault, as we didn't realize for a while that not every meow meant "feed me". Now we know better.) We then moved into a townhome with a small backyard and lawn. He was curious about the outdoors, but would only go out under supervision (his choice more than ours) and was very skittish.
Bells and I have just recently moved to Florida. Our new home has a decent-sized, full enclosed backyard. He has already lost some weight. He chases lizards, rolls around, climbs on my car, and eats more like a normal cat.
I would definitely not let my cat outdoors in an urban environment in which the risks far outweigh the benefits. That being said, if you and your cat are fortunate enough to live in a place where they can safely explore, I strongly, strongly suggest you let them out to play!
Tragedy in kindness
I always thought I should give my cat freedom. I imagined what it would be like to not have an expansive horizon as an adventurous feline. Of course, I opted for letting him outdoors occasionally. He needed, in my opinion, some sun and some playtime free of our walls.
It seemed like a grand idea, until he started getting ill. He began having chronic digestive issues, parasites and was vomiting as soon as he finished eating... later, his eyes were draining and his teeth began to disappear, one by one.
My cat has F AIDS. He will die. It is only a matter of time. I love him dearly. I thought I was doing something loving by allowing him to roam. Now, my dear feline companion has numbered days and will pass on. Please, I beg of you, keep your kitty indoors.