Docker vs Mesosphere

Docker is an open platform for developers and sysadmins to build, ship, and run distributed applications. Consisting of Docker Engine, a portable, lightweight runtime and packaging tool, and Docker Hub, a cloud service for sharing applications and automating workflows, Docker enables apps to be quickly assembled from components and eliminates the friction between development, QA, and production environments. As a result, IT can ship faster and run the same app, unchanged, on laptops, data center VMs, and any cloud.
The Mesosphere Datacenter Operating System (DCOS) is a new kind of operating system that spans all of the servers in a physical or cloud-based datacenter. Organize the machines in your datacenter or cloud as if they were one big computer. Save time, save money, and deliver applications faster.
Face to face in the news:

2014 - Microsoft and Docker team up to make containers play nice on Windows Server and Azure to keep up competition with Mesosphere

Microsoft and Docker are partnering up to ensure that Docker’s container technology will be fully compatible with the next release of Windows Server. Through this partnership, developers will have a native version of the Docker engine running inside Windows. While Microsoft has previously enabled the use of Docker on its Azure cloud, developers had to do a series of tasks to get containers up and running. Now, it will be much easier for developers to spin up Docker containers on Azure without having to do any modifications as they’ll will be able to access the Docker Hub within the Azure management portal.