I know nothing about it but looked at the links provided. It's interesting history and why 32mm became the industry standard for post-WWII rebuilding of European cabinets using mass production. Now we have IKEA flat boxes for assembly at the front door.
Ok, I'll be the devil's advocate and we can all have a good discussion about it.
1. Pros and cons of Euro-style construction versus traditional cabinet construction?
The big one is ease of construction for making a whole bunch. You can have many interchangeable parts because of how all the hardware connects. For example if you want shelves now, but later change your mind drawer slides attach in the same holes and vise versa. Also, depending on the system they can be stackable so the whole system can be modular. Economy of space. The same size framed cabinet and frameless will allow more storage space in the frameless. This is because face frames are larger than the carcass they are attached to. This leaves a gap between cabinets. Also the overhang of the face frame leaves dead spots inside the cabinet, that are a bit more awkward to use efficiently. There are more, so I will let someone else pitch the finer points.
2. Melamine vs solid wood?
The system works well with any material. Historically, solid wood was a problem since it has all been blown up. So things like particle board could be made where plywood and solid wood was prohibitively expensive and probably had some serious lead time issues. One of the beauties of this system came with the confirmat screw system. Here is a screw that can be used, and removed and reused even in particle board. It could be used without glue and provide the same strength in a manufactured wood product as a glued dowel. Particle board is roughly 1/2 the price of lower end hardwood plywood and high pressure melamine laminates are somewhere in between. But with melamine, your cabinet is finished when it is made, add some edge banding and Bob's your Uncle you have a clean looking strong cabinet. Right now, I am working with Birch plywood, but will try some of the other stuff before all is said and done. Again, someone else can probably come up with much more than this.
3. I can't justify the cost for Euro-style machinery (think Festool Mercedes) for a few one-off cabinets here and there?
Yeah, Festool. and Lineborers and Panel Saws Oh my!. You can certainly do this system with the Festool Lr32 system. It works nice with their router and such, but it not necessary at all. For line boring I tried the Kreg jig, but found it too fiddly and does a max of 6 holes at a time as long as your can set your clamps in the right place. I just ordered the Rockler one that does 15 holes at a time and includes the self centering drill bit (and can take different ones for doing different hole options this is about $35. And Woodhaven has an 800mm one that I may buy regardless which does more holes than I might even want to put in a 768mm (~30") cabinet but it doesn't come with the drill bit. It costs $35 too and they have a shorter version that costs less. This one will also use a router and collar of you are of that inclination. So that takes care of the lineboring.
I took a couple pieces of 1/2" plywood and glued and bradnailed them together and ran my cheapie craftsman c3 5-1/2" finish saw on it to make a perfect track. Strike a line, clamp it down and once again, Fannie's your Auntie you got a panel cut to perfect size. I assume this is not a new trick here to anyone, but if it is... then you're welcome. There are plenty of internet/youtube and otherwise plans for this type of track saw, as well there is cool idea for a "mini" panel saw that could be scaled up to a full size one that is horizontal rather that vertical so the saw rides in a rail system over the work. Not to mention cross cut sleds and wide panel jigs for the table saw there you have it.
Edgebanders can be expensive too. However you can get self adhesive edge banding in all sorts of colors, finishes and wood varieties with clippers (~$30) specific rollers (~30) or just a J-roller or a seam roller ($17-$2.50) and a side stripper that trims the applied banding to width (~$20). I have some cheap iron on edgebanding and an old travel iron (that sucks for ironing clothing) that my daughter was throwing away since my wife bought her a wonderful Rowenta (that does iron clothing well). It cost me $0 and the Goodwill is full of them. They also sell a tool specific to this task at about ... you guessed it (~30)!!!
You can join your cabinetry however you like. But, in this case using confirmats is the beauty of the system. There is a special 3 step drill bit that can be had from the teens to nearly 100 for a fully carbide model. Once drilled 3 screws in each side top and bottom and your 304 mm (12") cabinet is together. No glue, no muss no fuss. And you don't have to hide pocket hole screws or use bisquits or dowels to attach your face frame... because there isn't one
If I missed anything please feel free to add it. Otherwise, please know that I am learning this too. I still haven't bought 'True32 Flow Manufacturing' by Bob Buckley which is supposed to be the 'Bible' of this system.... pun intended if you desire