In the PSPSDK (Homebrew) we are using the Binutils 2.16.1 to assemble and link the code for the PlayStation Portable, however that release is getting quite outdated (3 versions have superseded it). The community and me have been updating the GCC and newlib to the latest stable versions and everything seems to work with the old binutils.
Will GCC produce better code with binutils 2.19? Why? Will binutils 2.19 produce better elf files and libs than 2.16.1? Why?
In general, you don't need to upgrade binutils unless you run into some bug fixed in a later binutils version, or need new features (such as linker build-ids).
In particular, GCC code generation is largely independent of binutils (except for constructs like __thread, which require certain level of support from binutils).
binutils 2.19 has a new ELF linker called gold which is multi-threaded, written in modern C++, and quite a bit faster than the usual ld linker. I'm not sure however about the work involved to adapt it.
Other than that, well new versions always are a good idea. Performance and bug fixes are likely to have been included, of course. I think i would certainly try it and if something goes wrong you can still backstep.