It's basically like..Say, you installed Kubuntu, you will have KDE which will run under kwin. You could alternatively install compiz and run compiz window mangement, so yes, you are running compiz in KDE. But if you were to apt-get install gnome-panel and install gnome classic or fallback, it's not getting a new set of compiz instructions. Once you switched sessions and turned on compiz it would be pretty much the same with exceptions for when a certain window manager is called upon by the application. The thing is, you really do not get any advantage with compiz other than the random effects mode and a niftier cube thingamajig, so if you are in KDE why not run kwin. If you have kwin and compiz setup they will go across both DE in their own fashion but be more stable in their native environment. So when you are all said and done, you now have two cube thingies . If you are trying to get the gtk+ window setup like previous Ultimate themes, etc, this is also possible with kwin, and compiz has absolutely nothing on qtcurve with kwin for window setup. It's not really about which is better though, but the fact that KDE doesn't need compiz in any way.
So alternatively, you could go into KDE and turn on kwin. You should be able to manage your desktop and fix compiz.
kwin
compiz