Too much is being inferred from those two videos.
@takethepoints made a good point about how the defenders at the next level are forcing outside in one and inside in the other. Another key difference is the initial running angle of the pitch receiver while moving along with the QB that is forced by the defenders at the LOS and where the pitch receiver starts in relation to the QB. In the first video, the two are running laterally alongside the line for a good bit to escape the defenders (Cottrell also had more ground to cover in order to get to that pitching position) and therefore Cottrell ran the "hoopla hoop" that
@Ibeeballin mentioned to preserve a lot of built-up momentum. A cut would not only lose that momentum but would risk running into the pursuing defenders. In the second video, the ball was pitched earlier without the extensive initial lateral run, so Lynch didn't have the built up momentum and therefore made the cut and then accelerated.
Long story short, while both videos contain a pitch play, the actual situations from start to end are significantly different.