There's a broad belief that Fiore and Liechtenauer taught the same general art, with personal emphasis changed to suit their manner of presentation.
For example, ringeck and von danzig cover much of the same stuff as Fiore: unarmored longsword, grappling, armored fighting, they just do so in a different order and with a different series of techniques presented (covering the same maneuvers, just in different ways).
For example, start with your right foot back, sword over your right shoulder. Step forward with the right foot past the left, and swing with the sword into your enemy's sword. stab him in the face. This is a ringeck/von danzig play from liechtenauer.
Italian, do the same thing, but without the step. Swing your sword across theirs, presenting the blade into their face, then step forward with the left foot and stab in the face.
Same move, different footwork. your blade clears theirs, and you stab them in the face.
Fiore adds in a body of dagger, short stick, and longsword in a single hand techniques that aren't presented in a single place in the german tradition - and he organizes his stuff in a very ascending order:
start with wrestling. then single stick/baton. then dagger (BIG section, the dagger). then sword in a single hand. then sword in two hands. then armored fighting, etc etc.
The german material is divided by broad topic,without a 'start here' pedagogy to it. Also, the german contains the masterstrokes, which are not set aside as such in the italian material, but rather exist within other cuts. Fiore divides the guards into far more positions than the german.
So tl:dr version - both will teach you longsword, and if learned well should both accomplish the same thing. The human body is the human body, and a longsword is a longsword. They have variation and will look different to someone who knows what to look for, but it's like the difference between different kinds of grappling, rather than the difference between boxing and muay thai.