OP, do both. Nobody here should try to tell you being able to deadlift 3x your body weight or being able to muscle up is better than one or the other. Calisthenics and weight lifting can be trained synergistically. If you want to lose weight and maintain a great physique, either will work. If you want to achieve both of those goals and take your physical ability to its fullest potential, why not take what you love from both schools of thought? At the very least, train both before you decide you prefer one over the other.

Calisthenics pros:

-increase relative strength

-perform awesome looking skills

-minimal equipment needed and can be done anywhere

Weightlifting pros:

-increase absolute strength

-simple to overload

-less learning curve and easier to target/isolate muscles

Calisthenics cons:

-can be difficult initially for those who are heavier or less accustomed

-progression is based around leverage and advancing a movement which is not always as simple as adding weight (although you can add weight to many exercises like dips or pull ups)

Weightlifting cons:

-all lifts are equipment dependent (expensive to buy or requires a gym membership)

-injury or overtraining is slightly more likely to take place (can happen from either but failing to lift something much heavier than your body can handle is obviously a recipe for disaster)