Google operated differently from Yahoo in the past.
Originally Yahoo was built on directories where people compiled the search items.
Google was built on linking keywords or page ranking method by computer code or algorithm which became a de-facto standard later for all other search engines.
Yahoo tried to imitate it but Google had been doing it for longer and had far more technical expertise in this area. However Yahoo is catching up and it will soon be there.Yahoo release a part of their engine in open source so developers can add capability similar to Google.
Google has added new Wiki tools or User generated /assist searching.
Some other companies even have semantic web searching code which means the search terms will be analyzed like normal spoken language.
Right now Google does not state it has Semantic Web. But I guess that it is already included in search algorithm.
So for now Google has the search engine which can take into account Directories, Human Input -Wiki like and also Algorithms and Semantic Web. Google has a hybrid approach to search. Also look at "Google universal search" .
Yahoo is lagging for now by about 2-4 yrs in search technology. They will soon get in line with Google.
In the future though search engines will all have similar strategies for search.
Google trumps Yahoo for now.
Read the Books "Google Hacks" and "Yahoo hacks" and you will see what I mean.
Google also offers more customization and integration of services and all necessary tools to get your office and home computer related tasks done faster. Google Docs, Gmail ,Maps,Google earth, Google presentations, Video chat and voice chat. A search engine should not only search internet but also intranet and all your online docs and there is no competitor for Google desktop and Google Gears from Yahoo.
Overall User experience is better and less time consuming in Google for now.
-Hope this helps.