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I'm not even sure it is right to say "hot on the heels" of Fedora, because the release of Korora 19 came so close behind Fedora 19.
As far as I can tell they were released on the same day, and their release announcements are consecutive on Distro Watch. I see this as a testament of the hard work put in by the Korora developers, and the fact that Fedora 19 had a smooth development cycle and was pretty stable for quite a while before it was released.
Korora is the "everything is in here" derivative of Fedora. One of the things that Fedora gets knocked for is the lack of some popular features and packages (let's not get into a discussion of the why and why not); if anything, Korora has gone to the other extreme, and the base distribution includes lots and lots (and lots) of packages.
The difference can be seen in: the size of the Live distribution images (Fedora is under 1GB, and Korora is over 2GB); the size of the initial installed systems (Fedora is about 3GB, and Korora is well over 7GB); and in the length of time it takes to install (Fedora takes about 10 to 15 minutes, while Korora takes more like a half hour).
But most importantly, the difference can be seen in the use of the system. If you really want something, and it is reasonably popular (or sometimes less than reasonably), the chances are that it will be included in the Korora base installation. Check the Release Announcement for a list of some major examples — here, I will just say that the things which I specifically mentioned in my recent are all included in Korora.
There are four ISO images available from the Korora Downloads page: 32-bit and 64-bit each for Gnome and KDE systems. I wanted to install the KDE version (I have Fedora Gnome installed, so I wanted the other one), but when I first tried to download it yesterday, it always gave me the Gnome image, no matter what I chose.
That problem seems to be fixed today, so if you were tearing your hair out yesterday, it's safe to try again now.
The images are hybrid ISO format, so you can dd them to a USB stick to create a bootable installation medium — but beware of the size, the stick has to be larger than 2GB. Once you get the Live system running, installation is exactly the same as previously described for Fedora, but takes about twice as long.
A word of warning: on UEFI systems, Korora 19 still uses the "fedora" name for its directory in the UEFI Boot partition. This means that if you are using UEFI boot, and you want to install both Fedora and Korora on the same system, you will have to take special precautions to prevent them from overwriting each others UEFI Boot information, and further to keep them both bootable.
This is not terribly difficult to do, but I assume that the situation is rare enough (how many wackos like me can there be?) and the solution is complex enough that I won't go into it here. Leave a comment or drop me a line if you really need to do this and can't figure it out.
Once installed, Korora has worked flawlessly for me. Every system, every bit of hardware, every driver — they have all worked straight out of the box. If you're not into reading release announcements and such to find out what the differences are, just install it and then browse around in the menus a bit. It includes a truly impressive array of pre-installed software, in every category. If you make the effort to try it, you are likely to love it.