I'm wondering whether the Nexus 7 version of Ubuntu ('Ubuntu on Android') supports the same software (i. e., VirtualBox, Google Chrome, LibreOffice Writer) as the desktop version. Is there any difference between the Nexus version and the Android version in terms of software support?
The Nexus tablet is not a full PC. It has an ARM CPU, which while having a pretty OK clock speed, doesn't necessarily perform well at some very CPU intensive tasks. It is designed for minimal power consumption. It also does not have the same instruction set as the x86 CPUs you're used to using in a PC. Therefore, some software will just outright not work or be available (such as VirtualBox), or may perform very poorly. You can see what packages are available by looking through the archive for binary packages built for the architectures
However, most software will be available, even though there are plenty of packages in the archive which only build on x86 architectures, or even on other architectures, but not ARM.
As dobey said it has a different processor architecture, so to summarise it:
Most software that emulates another systems like Virtualbox, VMWare or Wine will not work. Some, like Qemu will work as they have a processor emulation but much more slowly.
Most open source software will work, as most will compile fine to arm.
Most closed source software won't work, Adobe Flash, Reader, Chrome (as opposed to Chromium), commercial games, etc... as most companies don't ship arm binaries for Ubuntu.
In every case, expect poorer performance, specially in heavy packages like LibreOffice.