As outlined in the previous post, Kubuntu uses KDE while Ubuntu uses Gnome. Those are the default desktops but you can change it if you want (Kubuntu with Gnome or Ubuntu with KDE). Both have enough small differences that the only way to know which one you like is to try them yourself.
I personaly prefer Gnome because I find it more simple and still with the same level of functionality as KDE (and sometimes even higher). For example, in Kubuntu when you go to create a custom panel it gives you 5 different types of panels, but each one has a different functionality and restrictions. Ubuntu, on the other hand, just gives you one option (new panel) but you can do whatever you want to it.
In my opinion KDE has better native apps. than Gnome (they both use different apps.). Of course, you can always use a KDE app. in Gnome or viceversa, but sometimes you may face incompatabilty issues; I found that KDE apps. run just as well in Gnome, but I always have problems running Gnome apps. in KDE.
KDE looks better and has more customization options by default, there is just no question about it. Transparent panels, animated icons, more control over how themes look, color schemes, individual wallpapers for all desktops (Gnome only lets you assign one for all desktops), and the list goes on. However, trying to add extra customization (like extra themes and color schemes from the internet) can be a real pain; in Gnome you can simply install an extra theme with its theme manager. Another thing on looks is that Gnome runs XGL/Compiz (3D desktops and eyecandy) MUCH better than KDE; there is just not enough support for XGL under KDE at the moment.
I have had Gnome crash on me a few times and usually only a hard reset would fix it; I have had KDE crash even more times, but never to the extent of a full sysem crash (KDE has a good crash manager that detects and kills whatever app. caused the instability).
There are other little things that depending of your preferences may sway you to one or the other, so it's really up to you to make the final decision. KDE has a more Windows feel, but that's because it has a similar menu system. KDE tends to sugar coat everything while Gnome just gives it to you as it is. There is no clear answear so it's really up to you.