Great question! I would necessarily say it's better, it depends on your goal. But I'm going to list several reasons I think calisthenics is better.
1. You can work out anywhere at anytime.
2. You can workout all your muscles and in many exercises you combine several muscle groups.
3. It's completely natural.
4. You can do calisthenics pretty much all your life without getting injured(calisthenics strengthens your ligaments and tendons as well!)
5. It DOES bring great results, after all, you got guys looking like Chris from just doing calisthenics and are completely natural.
6. It's how the human body SHOULD be worked out, you maximize your strength and can reach your physique perfection(proportionally).
7. It's completely free! (Except if you want someone with experience to guide you into becoming the best you can be physically without making newbie mistakes)
8. There are thousands of variations of exercises for many purposes(so you won't get bored)
9. No equipment needed!(the floor doesn't count, and the bar is preferential, some people use trees, ledges, roofs as bars)
10. You become more athletic(most of the exercises make you more flexible and athletic, it can even be used as parkour training or martial arts training as well)
11. It regulates and stabilizes your body fat percentage
I bet there are many other reasons but these are just the ones I could think of right now. Hope to see other guys come help me out as well!