Well, I'm going to say that without a doubt it depends on when the first time you saw either movie was. If you saw Spirited Away when you were a kid, you got treated to an amazing movie, and you're now adding nostalgia into the factor. If you saw Toy Story as a kid you were treated to a pretty good movie that received massive hype and you're still running with the nostalgia.
In my opinion, Spirited Away showed what people could do with a budget and a great imagination. I mean, it cost 1/10[sup]th[/sup] of the price it cost to make Toy Story 3. However, the smaller budget didn't detract from the quality of the movie in any way and it's still one of my most favorite movies of all time.
But yeah, a large portion of this is really just "what movie were you raised on as a child?"