You missed one... the Berlin method. Virtually _every_ modern reefkeeper runs some variant of this... including all of those 'systems' referred to above. Live rock bio filter and a skimmer, it's not a new idea. Prior to the Berlin system, undergravel filters ruled the world. I seriously doubt there are many marine aquariums using this 'method' these days
Most 'systems' until a few years ago, struggled to maintain low nutrients. Carbon dosing (Red Sea NoPox, Vodka/Sugar/Vinegar, Bio-pellets, one of those little blue bottles has some form of carbon, I'm certain) allows us to supercharge the bacteria population by feeding it. Phosphate removers have come a long way in the last decade. Skimmers have gotten way better (my first was powered by a wooden air stone). The original Berlin system called for a boatload of live rock... most of us don't want a big rock wall anymore, so we substitute other forms of bio growth media... MarinePure, Siporax, Matrix, etc. With these advances in tools and techniques, we've gotten to the point that some folks are DOSING PO4 and Nitrate
These 'systems' all try and lay out a path... with or without sales benefits for the system creator, for folks that don't necessarily grasp all of the finer points of marine aquarium husbandry. They all make sense, I'm sure they all work, with the one caveat... your tank is not like everyone else's tank, and each one is going to need to be treated a little differently.
My new tank is going Triton. Why? A large macro algae refugeum, a good skimmer, a well balanced additive system, best of class testing... it makes sense to me. Add in the attraction of virtually no water changes, and, well... sounds great to me. Will it work? Probably. I've been at this a long time (in and out since 1984), and I've been fairly successful, no matter the 'system' I was using. The KISS folks above have it right... good basic husbandry practices and an understanding of how our tanks work goes a long way.