A full body workout is usually more biased towards the fitness aspect. You'll be burning more calories and generally working more muscles in your training time span.
This method of training generally provides a lower injury percentage. The reason for this is because everything is split up equally throughout the body. If we compare to a split training, where you'll go all out on a targetted muscle, that muscle will be sore and weak for X days. Whereas a full body workout will never get to that point.
Split training will be more on the bodybuilding side. You'll be targetting a select split of muscles throughout your week which will be completely demolished. For example, a bicep workout may consist of one compound movement followed by two isolations.
This will specifically target your bicep and barely nothing else.
Full body workouts are more oriented for fitness while split training is more for bodybuilding.