Hardware (even virtual hardware) is often initialized by firmware (the BIOS, pre-EFI hardware-initialization code in the firmware, or the firmware built into a device itself). This is especially true of video hardware and some other devices that are built into motherboards. Furthermore, the EFI provides a framebuffer driver for accessing video devices, which BIOS doesn't provide. This can influence how Linux accesses the video hardware.
In the case of VirtualBox, the entire firmware stack is different for BIOS vs. EFI modes. This influences how the Linux drivers interact with the (virtual) video hardware, because it will be initialized in different ways. FWIW, I run Xorg -configure to create a new /root/xorg.conf-sample file (or whatever it's called), copy that to /etc/X11/xorg.conf, and adjust it to use the fbdev driver. The VirtualBox guest drivers also sometimes now work under VirtualBox, but that's relatively recent and doesn't work for all guest OSes.
Something similar can happen on real hardware, too, although on real hardware, BIOS/CSM/legacy mode boots are usually done atop the EFI, so there could be more similarity between boot modes than under VirtualBox. Nonetheless, there can be differences between BIOS/CSM/legacy-mode boots and EFI/UEFI-mode boots. Because the former have historically been more common, the latter produce more problems, on average. This is especially true when using proprietary video drivers; for whatever reason, ATI and Nvidia have been slow to provide EFI support for their proprietary Linux drivers. IMHO, this is just another reason to avoid those drivers. (I've never been big fans of them, since they've always created more problems than they've solved for my uses.)
There are some other post-boot BIOS-vs.-EFI differences, too. In particular, EFI remains more accessible than BIOS, with something called "runtime services." The OS can communicate with the EFI to set NVRAM variables, use the EFI's framebuffer driver, and so on. At the moment, you're unlikely to use most of these features (except maybe the EFI framebuffer driver), but they may become more important in the future. One EFI feature that is important is the ability to set boot options via the Linux efibootmgr utility. Most Linux distributions use this tool transparently as part of GRUB installation, but you can use it manually to change boot loaders, to reboot directly into another OS on a one-time basis, or whatnot.
