University of Oregon Head Strength and Conditioning Coach James Radcliffe reveals some good research and analyses to this debate over which lateral step is better to train in his book Functional Training For Athletes At All Levels (2007):

In much of the University of Oregon Strength & Conditioning Program and Exercise and Movement Science’s experience and data collection, we have found simple answers to the debate on whether a crossover is better than an open step, or vice versa. In novice performers, the cross-over step has shown faster initial get-off. Video analysis reveals that without practice they push off with both feet and project the hips better than unpracticed open steps. The hips are often held higher as with higher-velocity running and speed cuts. In many sports, however, the crossover step can lead to improper positions on the field or court. Crossover technique may also lead to step sequences that are not as efficient as open technique due to other change-of-direction needs. Once trained in the art of projecting the hips from the open technique, the get-off times become more comparable, and may be more useful in certain positions and patterns on the field or court.

The purpose of the agility program is to teach body control, acceleration, deceleration and change direction skills. The agility program progressively utilizes cutting, change of direction and quick feet drills, using multiple movement patterns to teach participants how to better control their bodies, accelerate, decelerate and change direction. Initially two cone and three cone drills, like the pro-agility (5-10-5) drill using three cones, are incorporated to teach acceleration, deceleration and change of direction using the outside foot. Next, inside and outside foot cuts are taught using five-cone drills. As the training progresses, shuffling and combined forward and backward movement patterns are added into the drills. Speed cuts introduce inside foot cuts with a series of straight cones.

Use of drills like the figure-eight drill, can be introduced as an advanced power cut, and different variations of the pro-agility drill can be added using shuffling and combined forward and backward movement patterns. Transitional agility drills are incorporated by combining different drills and movements. Square drills can be designed in a vast variety of ways to challenge athletes by using unlimited combinations of movement patterns and cutting techniques. Transitional agility drills are designed to prepare athletes to be able to transition quickly in preparation for the demand of their sport. During upper level progressions, reaction agilities, like shadowing drills and coach response drills, are added to help improve reaction time.

Rope and ladder drills are used throughout the levels to help improve footwork and foot speed. Rest periods are held constant at 45 seconds between repetitions to allow adequate recovery. These drills are designed for teaching movement skills and the conditioning aspect is secondary. However, as conditioning improves over the the course of training, the number of repetitions per drill is increased.