It looks like gpu drivers problem and you are running live isos, aren't they?, they just come with the basics, whatever come with the kernel they ship, and some things to make the live iso usable (drivers wise not many, the iso would be huge), in some cases like yours it doesn't work with out problems.
In ubuntu, the installation screen didn't failed and looks fine to me, so , as I said, it's a driver issue, once you have installed your distro of choice, except pure os at the moment, updated it (I would go into tty in that situation) and installed the correct driver (exactly in that order), everything should be fine. For me you have that particular combination of hardware that for some reason makes things harder than they should.
Side note: in KDE they give you the option to change the render "backend", I dont remember the exact name, you can chose xrender, and some version of opengl, choshe what works the best for you.
