I've been using them for about 4 years now, both the lever and push types. Honestly one of the best inventions. Crimps are good too, but I prefer wagos in nearly all circumstances now. I was skeptical at first, but I'm converted to the church of wago!
Clear case so you can actually see the conductor is in the terminal (who can honestly say that they know 100% that their crimp terminal is on the conductor and the crimp doesn't have a manufacturers defect under the insulation without testing)
No fiddling about with screws that can de thread, or heads shear off.
Easy to modify circuits.
Easy to junction up to 5 (lever type) to 8 cores (push type) in 1 unit, try doing that with crimps or jb that easily.
Have you even tried to pull cores out of one? I have, it's impossible without intentionally doing it. Same as a crimp, but if you really need to you can separate wagos without cutting cores shorter like with a crimp.
TL;DR they have all the advantages of crimps and jbs but faster to install. The only disadvantages are cost (but time is money!), and slightly larger form factor than a crimp.
Now I can sit back and wait for my commission from wago... I wish!