Forget about crop factor unless you really have the need to compare sensor sizes, it is of no use if you only use it for one format. That video may state true facts but at the same time it's nothing you should really think of if you only use one format.
A 200mm F2.8 picture on aps-c is the same as a cropped fullframe one taken from the same distance and with the same settings. As cropping is very common in sports photography and the fact that you're more likely to crop a fullframe pic than an aps-c one taken with the same lens, same settings and same distance you will in many cases end up with two identical pics, no matter the sensor sizes.
---------- Post added 05-16-14 at 11:53 PM ----------
Originally posted by SpecialK Without looking at the video (won't play on this computer), the aperture stays the same for the same exposure. For depth of focus, there is a difference.
DOF will be different if you keep the subject the same size when composing by either using a different focal length or change the distance, yes.
If you use identical settings, keep the same distance and crop the fullframe pic to the same composition as the aps-c one, then they will be identical.