I agree with other commenter that the overview effect is real but an error. Just because earth is smaller than Saturn doesn't make it insignificant, or make our concerns - wars, religions, reality TV and all - petty. There is absolutely nothing of significance in Saturn that compares to what we have on earth. Significance can't even exist without life.
The thrust of Sagan's monologue was to encourage re-evaluation of religiously-motivated anthropocentrism.
To me, at least, it's less of "how could anything here matter when Saturn is so big?" and more of "does it really seem plausible that this vast universe was created for the benefit of some creatures on the surface of this little speck? Do you really think we're that special?"
Certainly it's possible to ride the Overview Effect all the way to nihilism, but it seems clear to me that unexamined anthropocentrism is at least as incorrect.
