Warning: This is all fairly new stuff, my machine locked up if I had run a Virtualbox machine prior to starting an xhyve machine. Don’t say I didn’t warn you ;)

Xhyve is a new hypervisor in the vein of KVM on Linux and bhyve on BSD. It’s actually a port of BSD’s bhyve to OS X.
It’s more similar to KVM than to Virtualbox in that it’s minimal and commandline only which makes it a good fit for an always running virtual machine like boot2docker on OS X.
This post documents the steps to get boot2docker running within xhyve and contains some quick benchmarks as well to compare xhyve’s performance with Virtualbox.

LXC (LinuX Containers) offers a lot of the advantages of (para)virtualisation with the added benefits that it can run on any kind of hardware (it doesn’t need hardware support for virtualisation) with lower overhead than virtualisation.
The virtual environments that LXC provides are comparable to a chroot but LXC adds control over the virtual environments resources like CPU-time and network-usage and offers more isolation.
This also means it’s only possible to run the same “family” of guest operating systems as the host. I.e. it’s not possible to run Windows using LXC, but it is possible to run different Linux distributions like a Debian and Fedora guest on an Arch Linux host.
Note that if you need a really secure environment LXC isn’t the right choice, stick with paravirtualisation like KVM or XEN instead.