I do think the main difference between Lydiard and Coe approaches is that Lydiard would rather you run more mileage at a slower speed to start and then work to improve your pace, while Coe would have you running at a faster pace for shorter distances to start and then work to add mileage.
Just two methods to the same end: aerobic conditioning supported by speed, followed by strenth, anaerobic conditioning, and then fine-tuning.
The problem I see with the Coe approach is that people get stuck in the concept of quality and never add the needed quanity as their condition improves. With Lydiard you start with quanity and the quality comes naturally as your condition improves.