Free-motion resistance training consists of any exercise such as free weights (i.e., dumbbells, barbells), flex bands, cables, bodyweight, etc. that does not limit your range of motion and is not restricted to a certain movement path. The benefits of this type of training is that you can strengthen not only the prime mover muscles but also the stabilizer muscles and you'll have the ability to perform a movement pattern unique to your joint movement. This type of training corresponds to how your body moves in life and is therefore conducive to functional training.
Which type of training type is better for you? The answer is that both can be good for the reasons previously stated. Consider incorporating both types of training techniques in your workouts. One strategy you might want to try is super-setting the fixed-path weight machine exercise with a free-path exercise. This allows you to push/pull a relatively heavy weight to target the prime mover muscle followed immediately with a free-motion movement to further fatigue the muscle along with surrounding stabilizer muscles.
Brian Danley, CFT
"Motivation is what gets you started. Habit is what keeps you going."