The Application
Yahoo is first of all a social networking service and the Yahoo Messenger application is chat client in which P2P voice capabilities had been added on later, for a feature called voice chatting. Skype, on the other hand, is a Voice over IP application in the first place, with added complementary features for chatting and social networking.
The Skype softphone client is relatively more compact and light, with a simple chat engine and basic features. This makes Skype relatively faster. Yahoo tries to do a lot of things in one single application. The Yahoo chat engine, with so many features such as emoticons, audibles, IMVironment, chatting background and others, makes the application cluttered and heavy on resources. I personally find most of those features useless, considering what they take, but if you like features and add-ons, Yahoo spoils you. Yahoo has no targeted and streamlined audience as Skype has.
Also, Skype has support for Windows, Mac and Linux while Yahoo lacks support for Linux at the time I am writing this.
The Cost
This is where Yahoo shines. Surprisingly enough, Yahoo offers better rates than Skype for local and mainly international calling with PC-to-phone calling. Calls start at one cent per minute for popular destinations. Skype’s rates are higher due to the fact that they charge a service fee. Whenever you compare the rates (because they are subject to change), consider the fact that Yahoo’s include VAT and are in US dollars, while Skype’s exclude VAT and are in Euros. Yahoo rates - Skype ratesThe Voice Quality
Skype’s voice quality is better. In Skype 4.0 release, enhancements have been introduced to give better voice and video quality at lower bandwidth, through the use of revised codecs. Yahoo has reasonably good quality if you have the necessary conditions for it, including sufficient bandwidth, but Yahoo’s voice and video quality might suffer in many cases.As a Social Networking Tool
Skype is more for targeted calling at appointed times. Yahoo is geared towards meeting people, with its chat rooms enriched with voice chatting facilities. Yahoo is one of the very rare services still allowing public chatting. These chat rooms are most of the time quite unethical, boring and to some extent, dangerous, but many find their account there.Skype is better for business than Yahoo. First, there is the more ‘serious’ edge; by its very name and reputation, Yahoo doesn’t really mean business, does it?

