Skype is maddening for me. I love Skype and that's why it hurts that they are going to lose to WhatsApp at this pace.
I use Windows phone so here's my experience with both
1. Notifications - Skype doesn't notify me if I get a call or message when I was offline. WhatsApp does immediately
2. Call connection speed - with WhatsApp, it's instantaneous for me. Skype takes forever especially if the recipient is running Skype on mobile
3. In a poor imitation of WhatsApp, Skype now groups my phone contacts with my Skype contact. Obvious, can't call them without Skype credit so it just wastes my time unnecessarily
4. WhatsApp is much lighter. It seems they are trying to remedy this in Windows 10 mobile by decoupling the messaging part from the calling part
5. Notification count. Even on desktop, the notification count is always 1. Even if I get 100 messages, it'll show 1.