Well, I think both Anime and Western Animation have their good and bad points. Me, I personally love Western Animation. But not the stuff they have out now. When I think Western Animation I think of films like the Little Mermaid (and many other traditional Disney films), Spirit, Fantasia, The Road to El Dorado, Anastasia, and other animated films like it. Those are Western Animation at its best, and the Western animation I would choose over Anime in terms of style (comparing it to a common anime style, since most animes don't come in the same style either like Western animation).
In terms of story, I think Anime will more often than Western Animation, take their audiences seriously. I think Western animated films (mostly) feel that it must either but some drawn out comedy or a family flick. And usually an awful comedy will by a TV show on Adult Swim somewhere.
So, yeah, I'm probably not making a good argument here, but I personally like both. It's not the style that matters or where the show or movie comes from, it's the story and characters. So I'll watch either. :) But I tend to look more towards Western Animation, just cause it holds more Nostalgia to me, and the characters are given more personality by their look.
I mean, one girl in this anime, can easily look like the girl from that anime. :b
So yeah...Western Animation. But eww, no Family Guy. No. The Western Animation I watch and love came out in the Early 2000s, the 1990s and the 1980s and the classics before then (ie. Silly Symphonies or Looney Tunes). Not these modern comedy shows from Fox or whatever.