AMK organizes most of the kits (EZ care) by injury and comes with a more comprehensive first aid book. If you are not highly trained the AMK kits will help you deal with a larger variety of injuries with more expert guidance. AMK tells you how to actually use the stuff (see Wound Care for example) and how to improvise materials.
AMK has two Physicians overseeing the development of the kits; one is a ER / Trauma Professor at Stanford plus a pro Rafting guide and the other is the founder of MedSail and a USCG liscenced captain. Atwater has no doctors, Buck Tilton is cool but is not an MD.
If you are trying to compare "bags of band-aids" there is less difference than if you compare the organization and expertise put into each kit.
If you are already an expert it probably matters less.