I'm not sure what you mean, but there are many western cartoons I've greatly enjoyed too. And to quell the argument quickly forthcoming, *my* personal definition of "anime" specifically is animation that is created by people who have grown up in and/or are apart of Japanese culture. Japanese people refer to all forms of animation as "anime", but it isn't exactly the same for other people in the world viewing the same thing. "Western anime" as you referred to it as, I would probably just refer to as western cartoons or western animation. There can be western cartoons/animation directly influenced and inspired by Japanese anime, even still using the Japanese anime art style, but I still wouldn't consider it anime because the ideologies, culture, and life experience is very different.
Now, to answer your question, I wouldn't agree western animation trumps eastern animation because the west largely views animation as a medium only for kids. The results are usually only kids movies or tv shows that, while still good, simply cannot be incredibly unique or distinct from each other because they are trying to appeal to a younger audience. The subject matter also becomes incredibly limited and censored as well. While Japanese anime doesn't have this problem, it is many times used for purposes not entirely indicative of good storytelling *cough* ecchie *cough*.
Now, if what you are ACTUALLY talking about is animation QUALITY, then that is another topic entirely. I believe that western animation as art and from a technical perspective can be incredibly good, however I'm not the biggest fan of the over reliance on almost exclusively using 3D/CGI animation as of late. And I have greatly enjoyed some of the older hand drawn Japanese anime movies and what not. But I'm no artist and I also know that anime can cut extreme corners and can look terrible from time to time. So that's more of a toss-up.
Does that answer your question or should I still grab the pitchforks?