Hey Justin, it comes down to the method in which we remove the nutrients from the system. Triton as I'm aware, uses natural means to consume the nutrients (your algae bed) while AF bacterial system uses carbon, zeolites, and a phosphate remover. In addition, if you go with the full bacterial system, you'll be liquid dosing carbon (similar to vodka, vinegar, or even biopellets which are solid) to feed the bacteria you're adding to the system. This is how you get the to a ULNS. If you go with the straight balling lite method from AF, you'll be using your skimmer or other means to remove nutrients.
As far as the AF salt mixes, you have to remember that AF has various methods you can follow. The regular reef salt is going to be used for a more traditional balling lite method. This differs slightly from the long-standing method of two part dosing by adding a third for magnesium. This is something introduced in Europe many years ago. If I had to guess, but someone who uses Triton can better explain this, is that the regular balling lite method is similar to Triton. The difference is that Triton tests the water to tell you EXACTLY what you should be adding back into the system. Balling lite, on the other hand, assumes that for every bit of alk, cal, or mag consumed by your system, it's using an equal part of the other trace elements. If your alk consumption has increased, that means it should be using an equal amount more of the trace elements. However, the Triton test can be used with any system and I know personally that I'll be sending test kits to Triton myself while on AF. It's the first of it's kind to tell you everything in your water.
If you move to the AF probiotic salt, you're getting the same salt, but they have added aminos and bacteria directly to the salt. You'll be replenishing these elements through water changes and dosing. This is where you'll be dosing bacteria and liquid carbon to the system, along with chemical filtration (carbon, zeolites, and phosphate remover). The mixture of bacteria and chemical filtration is at the heart of the AF bacteria-based system. I've seen a number of people switch from the regular reef salt to the probiotic, so this might be something to consider if you're unsure today.
As far as your goals are concerned, it sounds like you want a proven system with minimal amounts of technology to drive it. I think you'll be able to do that with any of the systems if you're going to reliably dose manually. The reason most people add additional technology is because we are kinda lazy.... and/or it's a cool toy to use. Someone said it earlier, it's two very different ways to reefing, but both have successful tanks running them. I might be rambling a bit but this is what I've read as I'm preparing my system. You've got some great resources in here who have used Triton and there are a number of AF users actively using the system, hopefully they can chime in and give you more hands out experience, guidance, and advice.
edit: if you use the regular AF salt, you do not have to use the balling method. It's a great product regardless. You could use the probiotic, but it's probably a waste of money if you're not doing the full bacteria driven system.