My cent: Linkedin vs Yammer would in the short term by like the new Facebook at Work vs the familiar Facebook network.
The consumerbased solutions (Linkedin + Facebook) are based on your private identity and your private network, while the workplace solutions (Yammer + Facebook at Work) are based on your employee identity and your workplace network.
You may see some functionalities being exported/imported between Linkedin and Yammer. You may even see some integrations, for instance people directories in Office 365/Yammer enriched with Linkedin information. But as solutions, offerings and networks they will be kept separate.
I would therefore keep investing in Yammer and focus on the ongoing integration with the Office 365 suite and upcoming integrations with Office 365 Groups, Skype, Teamsites etc.