Last time I checked, I got impressed by the wide platform support, once you go down the tier list (https://doc.rust-lang.org/nightly/rustc/platform-support.htm...). What "obscure platform" specifically are you thinking about, that is currently missing from those lists?
However, there is now a Rust codegen plugin for GCC, so even this disadvantage is now basically moot.
Rewrite all the things!
LLVM doesn't have an equivalent annotated list, but it is missing alpha, bfin, c6x, fr30, frv, gcn, h8300, ia64 (aka Itanium), lm32, m32c, m32r, mcore, mep, microblaze, mmix, mn10300, moxie, nds32, nios2, pa (aka PA-RISC), pdp11, pru, rl78, rs6000, rx, sh (aka SuperH), storm16, v850, vax, and visium. For its part, LLVM does have some targets that GCC doesn't have (mostly related to GPU compilation).
The "big" targets that GCC has that LLVM lacks are Alpha, Itanium, PA-RISC, and SuperH, with Itanium being sufficiently weird that it's pretty firmly in the "fuck this" category from a maintainer's perspective, and people are actively ripping out support for it.
There are many. Two big ones are Alpha and PA-RISC. NetBSD and Linux continue to support both. Linux distro choices are pretty much limited to Gentoo though.
2. LLVM does not support as many backends as GCC does, so even if you did get 100% of the LLVM supported backends up and running, you'd still be missing some.
But even for the architecture part there can be differences. For example, my understanding is that a lot of the calling convention details need to be handled by the frontend in LLVM, leading rustc to duplicate logic from clang here. Things like varargs FFI with C code can be particularly gnarly.