Recently I've found myself comparing a lot of features and application from the two giant search companies. Each has an incredible lineup of stuff, so much in fact that it's near impossible to compare both on an even playing field.
The skew, I think, leans towards the side of Google, where they have Earth, my Outlook saving Desktop, and
YouTubeVideo. Each being very cool applications that I find myself using regularly. Although Yahoo is the owner of Flickr which is my single most used web application, and probably will be as long as I dabble in photography, and they maintain the Widget Engine which is another useful peice of information software.
Staying away from the fringe, I'm going to compare the three core applications that both companies have done for a while, which I and a few other people use regularly; namely: Mail, Calendar and to a lesser degree finance and a customizable web page.
For mail, I think Google has it in the bag. Both e-mail applications are rather slick and easy to use. Both providers offer a silly amount of space for the typical user, but Yahoo makes it a little tricky to figure out where you are sitting. I really like Yahoo's RSS integration, but with google's reader being out in the wild, I don't think this is much of an edge. G-mail wins with a cleaner interface, and a couple very easy to implement features like forwarding all your mail to another address, secure RSS of your mail and POP access if you really want it. Yahoo may implement these features, but their interface is too clumsy to figure out how to do it, and if I can't find it, I'm sure there is others out there who can't either.
For the Calendar battle, I used to be solidly in Google's corner, but recent uncoverings have me on the fence. Once again I find Google's interface to be cleaner, and easier to use. I love being able to share my calendar online with my friends (Yahoo does this too, but all my friends use Google), as well as all of the public calendars (like the Rugby World Cup and Calgary Flames schedules). Google was my clear leader, until I found out how well Yahoo integrates it's calendar into it's other applications, namely finance.
This is really where my comparison started. Until recently I have been keeping tabs on my portfolio at E-northern with Globe Investor. The Globe and Mail has been pulling more and more of it's services into it's gold package, and the site has become much less useful. I decided to set up my portfolio tracking on both Yahoo Finance and Google Finance. Both sites have a plethora of news, and pretty graphs, as well as streaming quotes and portfolio management. The problem is that Google's portfolio management is useless. Sure you can create a portfolio and track it, but you can't add all of the real world equities that you have. Take Big Rock (Yahoo's page: here), a fully registered income trust with a six year track record. Sure enough you can get a quote from Google's site, but you can't add it to your portfolio. As a matter of fact: it doesn't look like anything on the TSX can be added to your portfolio. This makes tracking gain/loss on 80% of my portfolio impossible, which in turn makes google's finance page useless for my needs. Yahoo takes a clear, and definite lead in this category, and their win spills out to other areas as well.
With my portfolio entered correctly, I can display it correctly on my custom homepage that Yahoo provides, which I can not do with Google's version. This means that my Yahoo home page is again way more useful than my equivalent version on Google. Both homepages have a stupid amount of addable content from weather, news and integration with their other applications, but Yahoo doesn't stop just bringing everything to the homepage, their applications can talk to each other. Take the Calendar and Finance for example, looking in my Yahoo Calendar I can see the dividend payouts from stocks in my portfolio. Google doesn't offer that, and with the state of their finance page, I don't think it's high on their priorities.
Now that I'm done the wordy part, I can say that you can't just pick one of the two giants for everything. I've picked up Yahoo for finance, but still maintain Google for my Mail and Calendar needs. Although Yahoo did wrestle my homepage away from Google. For the time being.