I think the two services, while doing basically the same thing are very different from each other. Whatsapp is becoming pretty ubiquitous – everyone seems to have it and use it. I personally use it to communicate with friends and sometimes even for business purposes.
However, if you want to call a landline or someone who is not on whatsapp you simply can’t. With Skype, although you often have to pay a fee, you can call any phone number anywhere in the world. This is the main difference between the two services.
As for call quality, although I haven’t made a point of comparing the two services, the general opinion is that Skype requires better Internet connections and provides better call quality too. This seems rather normal since Skype has been around much longer and it is a service that caters to both businesses and individuals. Also, Skype has many more features like video conference calling, international plans, business features.
It all depends on what you’ll be using the service for. Or why not use both?