The quick summary is VirtualBox vs kvm/qemu is a classic commercial product vs open source comparison. Without going too deep into the actual architecture, VirtualBox is much easier to get started with (although check out something like Proxmox), but qemu is much more powerful. AFAIK, there are no features in VirtualBox that can't also be done with kvm/qemu, but there's a lot of things that can be done with kvm/qemu that can't be done in VirtualBox.

I say kvm/qemu because the actual hypervisor is kvm, while qemu is used for control and device emulation. qemu can also emulate full machines, which is obviously much slower but can be extremely useful.