Is there any performance difference between the VMDK and VDI virtual disk formats with Virtual Box?

I don't think so - for example, this blog post claims the following:

Both formats are wrappers around a raw disk image so raw performance isn’t really at issue.

However, it also says the following:

VirtualBox has to mount a vmdk image as a writethrough disk, which means it loses things like snapshots and possibly driver performance.

I don't know if this applies to the newest version, but it sounds like you should go with VDI.