Note: You can skip the first bit of this post if you want and continue on the second paragraph-ish thing.
I've tried both Ubuntu and Kubuntu with my laptop, however, booting Kubuntu from a USB stick (which is as far as I got with it) it turned to a blank screen because my laptop doesn't have any decent Linux drivers, but with Ubuntu, which is actually what I use for school, I am fine as far as the graphic card.
Err- anyway, on to an actual reply that stays on topic: The only REAL different between Ubuntu and Kubuntu (as far as I've seen) is that Ubuntu possibly has more driver support, (or AT LEAST supports different types of hardware than Kubuntu does.) and Ubuntu uses the "GNOME desktop", and Kubuntu is based off of "KDE desktop" - I couldn't tell you a difference really because I've only used Linux distributions based off of GNOME. (I guess you could try looking them up on Wikipedia - that might help.)
Also, I think Kubuntu has different "packages" in the package manager than Ubuntu for software, but I believe they both can install ".deb" files as they're based on Debian.
Sorry I can't be much help. I'll see if I can boot Kubuntu off of a jump drive on my desktop and point anything out to you about differences. (EDIT: I was able to boot Kubuntu on my desktop computer from a jump drive, but unfortunately my monitor wasn't supported and had screen centering problems. Mainly I was only able to see about half of the actual desktop environment.)
In conclusion from my tests with questionably supported hardware and not being able to test Kubuntu properly, I would say in conclusion to my stupidly stretched out post: Try both, see which one, if either, fully supports your computer. You can put them on USB sticks and boot from those if you have one that's about a gigabyte or two big and boot from that without changing your current data. Although if you're going to buy a new computer or something and it'll come with either or, I wouldn't worry about hardware issues as it would be most likely a slightly modified version of K/Ubuntu and would work with the hardware the computer comes with, I would just recommend you read up on them both if the aforementioned is the case and decide which one you like better. (I'm not sure how much my post matters as I've only been able to try Ubuntu with actual success, but I hope I at least helped a bit, or otherwise gave you a few laughs about my repetitive typing and most likely somewhat numerous grammatical errors.)