The author of the article explicitly says, "This isn't to say that they're going to replace virtual machines." and I agree - there's no point in pretending like they're solving all of the same problems. I guess you could say that containers are an optimization of some use cases of VMs.
Really, the only reason to use virtual machines is if you truly need different OS kernels.
[1] http://www-03.ibm.com/systems/power/software/aix/sysmgmt/wpa...
LXC is mainly a way to manage multifunction servers in a clean way, and Docker is a nice tool to help you leverage LXC without having to learn all the details. The nicest thing about Docker is that a developer on Windows could set up a VirtualBox VM with Linux, run all the same Docker Scripts as the production server, and have a reasonable facsimile of production to do testing.
I still do not understand the use case of live migration though...
E.g. You may have multiple VMs running applications like sharepoint, exchange, zimbra, or whatever, all on a host. You want to perform some planned maintenance on the host, e.g. update the firmware, add memory, upgrade the hypervisor, etc. You place the host in maintenance mode and the VMs are migrated off the host onto another one within the cluster without having to resort to planned downtime.