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Setting up a server running many XP VM's. What are the advantages and disadvantages of having users remotely connecting to the guest machines by Virtualbox Remote Display vs by the XP native Windows Remote Desktop?

Rather than advantages/disadvantages, their use cases are totally different.

VirtualBox Remote Display is about accesing the console of the Virtual Machine. It would be like actually connecting to the physical screen, keyboard and mouse of the computer. You don't need any networking to work in the guest, most low level issues will only be solved via the console (think about a corrupted MBR which you need to fix), also when you install the OS.
The remote display protocol is RDP using the extension pack, and offer somewhat some features (like clipboard sharing, usb devices acces, etc) but is not optimized like the real Remote Desktop protocol, and makes no attempt to be - it will send screen buffers update in form of image, and not in form of objects where th rendering is done on the client side. So anything GUI related would be slow, take a lot of bandwith.
Also, in term of authentication, you do not directly use the Windows mechanisms, but rather some external modules from VirtualBox.
to sump up: VirtualBox Remote Display is typically for admins.

On the other hand, Windows Remote Desktop use the native stack of Windows, but requires the guest networking to be working. The user will actually log to a proper remote session, be able to use all the feature of the RDP stack, have optimized display mechanics and use native authentication mechanism.
To sum up : Windows Remote Desktop is typically for end-users of the VM.

So if I'm understanding correctly, by having the end users connecting to their XP VM using Virtualbox Remote Display, the VM's no longer need networking enabled (assuming they didn't otherwise). Sounds like a security advantage when we're talking about an unpatched and out of support operating system. However, if the XP VM's already need networking, Windows Remote Desktop is prefered for the end user connection. Correct?

Well, are the VMs on the same hardware as what they connect from or remote?

The server running the XP VM's is on the same LAN as the workstations the users will be using to remotely access the VM's. Administration of both the server and VM's will also be done from a workstation on the LAN. Other than (potentially) for remote access, the VM's don't otherwise need any network access. However, both the server and the workstations need internet access from behind a NAT router.

Then the Windows Remote Desktop is the obvious choice.

Please note that you can have the XP guests connected to the LAN but blocked from the Internet by setting a fixed IP address in each guest, blocking those IP addresses in the "Access Restrictions" page of the network router, and using Bridged in the guest network settings. Make sure the users are restricted from changing the IP address of the guest. The guests will be able to connect to everything on the LAN, but web browsing attempts and Auto Updates requests will launch into an endless black hole...