Both weight lifting and calisthenics follow the same philosophy: resistance training.
This means that they are both following a legitimate path. I would personally advise against certain Youtube workouts where the entire video is just a warm-up routine.
However, some people prefer weight machines, or free weights at the gym, while others prefer doing bodyweight workouts in a park, or with furniture at home.
I personally think both paths lead to great results, so it really comes down to personal preferences:
1) Calisthenics is better than increasing the functionality of the human body;
2) The path for linear progression for weight lifting is less confusing; this also means bodyweight workouts have more varied movements and thus can be more fun;
3) Free weights exercises are better than targeting isolated muscle groups;
4) Calisthenics workouts are much cheaper since you do not have to purchase dumbbells or pay for a gym membership;
5) If you feel uncomfortable in a gym environment with people exercising around you, calisthenics will give you more freedom;
6) Rock climbing is also one form of calisthenics. Rock climbing and bouldering are great forms of using your body weight to move around and top-notch rock climbers have elongated muscle curves and are freakily strong. And it is incredibly fun with potentially endless routes to climb through.