What are the benifits for each considering in most cases it depends on which doctrine better fits your circumstance, however what are the strong points over each other?
I played as Canada using Grand Battle (Assault) and Mobile Warfare (Mobile Infantry+Modern Blitzkrieg) in separate scenarios. I used Superior Firepower, too. I find Mobile Warfare pretty good, if you plan to use mobile infantry (motorised and mechanised). It might be tempting to use the desperate defence tree to get 5% extra manpower for a country with good industry and low manpower pool (like Canada). Mobile warfare is optimised for offensive warfare, not so much for defensive. I find the bonus to speed nice to have, but you can also overrun enemy infantry division even with their default speed.
Superior Firepower is more suitable for use with leg infantry. It'S famous for its great bonus to soft attack, plus additional organisation to support units.
I like both doctrines. You need to know which strategy you want to employ and choose your doctrine accordingly.