Yahoo added a tab for Video Search to their homepage yesterday, presenting the feature to the millions of regular yahoo users (it was available for some time through the next yahoo page).
This is a fairly decent search tool, presenting video of TV shows from their partnership with TV Eyes, along with clips from around the Web in a familiar search interface that gives users what they expect to find when they search on it.

It contrasts vividly with Google's simultaneous announcement of Video Search beta, which takes a totally different approach; maybe so much so that not many people will have a use for g's offering.
Google does not actually present you with a video file in any of the results (as yet), nor even a link to a webpage that may contain the video file you're looking for. Instead what it gives you is the information surrounding the video you search for, closed caption text, a screen capture image, and if you're in the U.S, a schedule of when the show will air next in your location.

It seems to me to be a rush release for Google (it's the only explanation for releasing video search without any videos), just a part of the healthy competition between the two companies; Yahoo have the clear winning product at this time insofar as something people will likely have a use for, though Google have secured assets that will probably make their tool a winner in the long run.

With the participation of the U.S. TV stations involved (listed here), they have continual access, through satellite antennaes & dishes installed at Google headquarters, to all of the currently broadcasting shows as well as the closed caption content that is transmitted with each show, archived back to last December - a trove of non-internet content they'll be able to wrap around actual video clips when they're made available.

Google are focusing on their main aim, to go for the content that's not yet available to people through the 'Net, in the same spirit as the Print project, that will see them go into top libraries in the U.S., scan the collections of books and make them available online.

At the moment there's not much use to the G video site, there are no clips, no access to the complete closed caption transcripts (only the segments containing your search query) - it's main use will probably just be as a handy TV guide-like service for people in the U.S. The one glaring advantage Google have is their presentation of all the information that is currently available - hands down much better than Yahoo's, which only gives you a screen capture, the file name and the size of the clip.
For comparison, check these results for the smae item:
Y:60 Minutes Google | G: 60 Minutes Google

Another similar impressive piece of technology has been available for some time - the blinkx TV video search. Their service disposes of the need for the closed caption content altogether, they've created their own automatic transcription technology that interprets the content of terrestrial/satellite tv shows & radio broadcasts in real time into their index, along with media content from the Internet.
blinkx TV is available here and the white paper explaining how it works is available here (.pdf)

More info:
· Yahoo search blog: Video Search Goes Mainstream
· Google blog: We're tuning in to TV
· Press release: Google Tunes Into TV
· Google Debuts Video Search
· Yahoo!, Google Thrust Video Search Into Spotlight
· Geeking with Greg: Roundup of comments from the blogosphere
· Yahoo Next - Yahoo research labs
· Google Labs