Since they both use same gecko engine there is no difference in page rendering. The difference comes in in usability and customization. While we all know that you can edit pretty much anything in Mozilla -- skin, menus, options and whatnot -- it is kind of hard to figure out what, where and when.
It's easier with K-M, and, for many users the most important difference - speed. K-M doesn't have to parse loads of XUL and resource files files to draw UI (user interface). Mozilla does because it needs to be platform independent, therefore it needs to rely on its own resources for putting it all together in realtime. Thats one thing that makes it always slower than UI which uses OS native widgets and elements.
You can change menus, popups & other stuff in Mozilla too but compare it to K-M and you'll see the difference. Just in other thread folks just added "google search for selected text" capabilty to context menu. You can do it literally in 3 minutes without any previous knowledge. Try it with Mozilla and see how long it takes
So most likely you want to keep using Mozilla when you're happy with its speed and options it gives you. You might want to try K-M when you want to do little tweaking here-and-there, add your own menus, design new buttons for yourself or just are too imatient to use Mozilla on slower computer.