FWIW -- Looking at my contributions to this thread, it appears (I think) I'm handing down the Truth on Tablets of Stone from on High. Sorry about that, Chief. Informed opinions only. It's an interesting subject, the back and forth is fun. Don't confuse conversation with TRUTH. First, there's no best way. The most selective we can get is several best ways for a given person and her or his knives. So Truth is elusive. Tablet engraving, stone and high are two different threads.
Yeti-ji -- Edgemaker uses a set of progressive "sharpening steels," that remove a lot of material and leave a lot of scratch on your knives. There are steels that "hone" instead of sharpen and don't remove material -- and you should have one -- but they don't sharpen. On the other hand, if the steel marked "hone" removes enough material to polish a lot of scratch off, it's removing material. Which is exactly what it does. Finally, even after the last stage, although the knife is sharp, it has a very "toothy" feel which I don't like -- especially for fine work like batonet, julienne, fine dice and brunois.
Also -- a V steel with two rods, such as the Edgemaker is not the same as a single rod steel when it comes to straightening potential. It doesn't do the same thing as a "honing" steel; the principal purpose of which is straighten and "restore" the edge, not sharpen it.
Those fine cuts are cuts I make all the time as part of my home cooking -- because that's how I learned to cook. Breaking things into leaves, then sticks, then dice is something I do more or less unconsciously. You may not make these cuts ever -- finding them overly fussy, for instance. I do more butchering and fish prepping than most people because I buy from Asian stores that provide the quality and freshness I want, but not the Western cuts I use. These tasks are best done with a smooth, polished edge. Plus my knives are more than anonymous tools to me. My K-Sabatier au carbone are almost forty years old and you can't tell them from the same models I bought for my kids five years ago.
If I sound like I'm slamming your system, I don't mean to. If you like the edge you get -- and it's a no nonsense edge a lot of people do like, that WILL by God cut a tomato -- you should stick with it. I wouldn't recommend it to a pro though because these sort or edges tear more than they cut, and don't do fine work well. I also wouldn't recommend it to someone who means to keep their knives for a life time.
Returning (almost by accident it seems) to the theme of this thread -- the restaurant style of cutting with its lyonnaise, julienne, brunois cuts is what Sparkling Burgundy may be doing. Her knife edges should help, not hinder.
angrybob -- The 120 uses a diamand disk shape, a second diamond disk to sharpen and a strop to polish. The 130 uses a diamond disk to shape/sharpen, moving steels to strop/polish and a strop to polish. It's slightly less aggressive -- which is fine since the machine does the work. The idea is that a knife finished at stage two may be considered finished, or stage two can be skipped altogether. The user gets three final profiles -- 1 + 2 + 3 ("trizor" edge), or 1 + 2, and 1 + 3 (double bevels) -- each one appropriate for knives meant for different tasks. I've got to say though, that IMO, they're all more obtuse than I like for my knives -- which is why I still use stones.
My stones "disappeared" four years ago during a move, and I considered changing to a variety of different systems. I used my folks' discarded Model 100 (first generation -- 3 stages but no scissors or serrated) Chef's Choice for almost a year while I contemplated their replacement. The convenience is addictive. (A lot of what I've learned about stones is information I gleaned during that time, researching and trying different systems.)
The big step up between the 120 and previous generation machines is the knife hold/guide system. The old magnetic system was prone to slips and mistakes. I think the 120 is a great unit, but everything else being equal would rather have the 130. However, although I do miss the luxury of ease, neither fits my needs as well as other systems. As good a time as any to say, the most important part of any sharpening system is that it gets used as soon as its needed. Inconvenience inevitably becomes procrastination.
Chef's Choice introduced a three stage "M15" around Christmas last year that was designed to convert European style knives and their obtuse edges to the more acute, Asian style 15 deg edge -- and keep that edge sharp and polished. It sounds interesting, indeed it sounds like an ideal edge for quality European knives. But for some reason seems already to have been discontinued.