You wonder which search engine you should use and why. Many people have written about it and I guess largely it is a matter of preference - you stick to what you have used for a while, and media frenzy -- Google has been over hyped a lot recently and this gives it a significant benefit. However, the quality of the search results served by the two rivals is largely the same in most measurable statistics one can think of, and in some Yahoo! is superior to Google. One such statistic is the quality of spelling correction, e.g. when you type "Arnold Schwarzenegger" in the search box, only few people would know that you spelled it correctly but even if not, the search engine would provide a corrected suggestion. And Yahoo! Search gives better corrected suggestions, more often than Google.
What is also true is that Google is typically doing a better job on a class of queries called navigational queries, the ones that have an explicit intent, i.e. someone who types in "Amazon.com" in the query box, or even "Amazon" alone, most likely means the popular web site than the river. However, once you average across all queries the two engines look equal.