I think what you're really asking is what distinguishes the early models from later ones. There are a number of key factors. First, the Z1 was a huge step up in power, which allowed it to develop a racing pedigree in its day. Later years had to compete with models built by Suzuki and Honda, among others. There was little to distinguish between them, and the KZ series was no longer dominant at races.
Second, it had classic styling that is admired and copied even today. Suzuki copied it shamelessly with their GS series. And third is nostalgia. When I saw my first Z1 I was captivated by its look. I vowed then and there to buy one when I could, and two years later I did. A few years later, like many bike enthusiasts I had different life priorities and I left biking behind. Flash forward 40 years to my return to motorcycles....there was only one bike I wanted to buy. And I did.
As an owner of a Z1 (two actually) and a KZ1000, my opinion is that the KZ is far better for riding. Better handling, particularly for cornering and a bit more comfortable. My only wish, and this is driven from being much older and much more demanding of comfort...is that Kawasaki would develop a softer seat and moveable footpegs to accommodate my stiff knees and hips.
So to summarize, style, power, nostalgia and racing pedigree.
I have a couple of Z1B's restored, an '80 KZ1000LTD restored, a 1981 KZ550 restored and a 2008 KLR 650 for off road fun. My wife has a 2019 Suzuki DR 650 for on and off road.