Free weights offer a greater opportunity to generate momentum in an exercise. This is NOT necessarily a bad thing. There is a time and place where this quality can be useful. For more on that, read Momentum: Proper Application for Resistance Training.
An important thing to keep in mind is that momentum occurs in both directions; both the concentric and eccentric portion of the movement. This means that in certain exercises where there is a greater risk of injury in the lengthened position (squat, bench press) if an excess magnitude of momentum occurs that is greater than you can stop within your active range.
However, it also allows you to potentially change the resistance profile of certain exercises just by changing your intent on the concentric portion. An example of this would be using a Tempo Super Set.
If you want to create momentum on the concentric, such as in some neurological training for strength gain, then free weights can be a good option.
Cables limit the amount of momentum that can be produced. It also means that you can perform faster reps with minimal loss of tension, especially depending on the ratio of the pulley system being used.
Science Alert: 2:1 pulley systems effectively take ½ the force to move a given load. So if the weight stack is 100lbs it will only take 50lbs of force to move it. The end of the cable that you are pulling on will also move 2x the distance that the weight stack will move. Similarly, a 4:1 pulley system takes ¼ of the force to move a load and the end of the cable you’re pulling on will move 4x as far as the weight stack. This is why a 4:1 pulley will limit your ability to create momentum more than a 2:1.
This can be very beneficial for metabolic training where you may not want longer eccentrics perhaps to minimize mechanical damage or to just have a greater percentage of your work be concentric, thus creating a greater energy and metabolite production.
The other factor introduced by cables is friction created by the pulleys. This friction is often negligible but when you have more pulleys between you and the weight stack, it can add up a bit. This friction will actually make the resistance slightly greater on the concentric and slightly less on the eccentric.
This can also be beneficial in metabolic training where you want to limit potential mechanical damage and maximize metabolic stress. Now, don’t put too much weight (lame pun intended) on the effect of the slight de-load on the eccentric and limiting mechanical damage as it is very small compared to the magnitude of other factors; training in the lengthened range of a muscle, overloading a muscle in the lengthened position, training under great fatigue or with multiple sets to failure. It was mentioned to complete the considerations as accurately as possible.