It has been nearly two years since I tried Fedora, Manjaro and Ubuntu MATE on the Raspberry Pi 2 & 3, and there have been a lot of changes since then. Most for the better, such as the introduction of the Pi 3B+, but a few for the worse, such as the end of the Manjaro Pi development. So I think it's time to take a fresh look at this.
But, first, why would anyone even want to do this, when Raspbian Linux is available, free, and supports all the special features, quirks and capabilities of the Raspberry Pi hardware?
Well; the most common reasons seem to be that users want to work with a "familiar" distribution, meaning one that they are already using on a PC, such as Ubuntu. Another common reason is that companies have "standardized" on a specific version of Linux for servers, desktops and laptops; this is frequently the case with SUSE and Fedora, for example. Yet another reason might be a specific use of the Raspberry Pi; for example, Kali Linux for penetration testing. Finally you might just be curious (or masochistic) like me, and want to see how (or if) all of this works together.