Lift with free weights to gain the most strength and mobility, while getting the best body composition benefits. Research suggests it doesn’t pay to rely on body weight training or ‘suspension’ training in which you lift your body against gravity.
The reason is that most body weight exercises are either too easy or too hard to produce any significant benefits for the average trainee. For example, you have to be very deconditioned to benefit from body weight squats because the load of your own body is not enough to elicit measurable strength or body composition benefits.
A recent study found that even in elderly people who had knee osteoarthritis, body weight squats were not sufficient to promote physical-functional benefits or decrease knee pain. Doing the squats on a vibration platform did produce strength gains because the vibration stimulus provides additional overload to the muscles that is appropriate for people with fairly serious dysfunction.
For the average healthy person, training with weights is more beneficial and practical than using a vibration platform. For well trained people, other body weight exercises such as chin-ups and push-ups will be too easy if weight isn’t added. On the other hand, the average overweight or sedentary person will find body weight exercises like chin-ups and push-ups to be too difficult to even perform one properly, making free weight training favorable to build up strength.
Similarly, although suspension training can overload the body in certain cases such as the inverted row for training the back, it shouldn’t be relied on as the sole training stimulus. Reserve body weight and suspension workouts for when you don’t have free weights handy, and rely on the traditional lifts for best results.