Both offerings can run FOSS, straight up.
Apple: Install bootcamp, then install Linux
Chromebook: Install MrChromebox, then install GalliumOS (a fork of xubuntu for chromebooks)
Apple gives you more choices, because it offers more standard hardware, and has a real HDD, but chromebook has ASTOUNDING battery life, and is very cheap. (Sticking a really big microSD card in, and mounting it as /home with TRIM enabled can get a lot of mileage out of the otherwise space constrained chromebook ecosystem, which is what I did with my Samsung CELES.)
Either way, you nuke the proprietary closed OS off the device, and run as close to pure FOSS as possible. (MrChromebox installs SEA BIOS based coreboot image for legacy boot mode, which is itself FOSS.)
Other than maybe some kind of contractual agreement to get the hardware, there isn't that much in the way of a school running free software and still leveraging this bidding war in their favor.