One practical difference is that software emulation almost always runs under an operating system and all sorts of cruft which can add latency and jitter. An FPGA just does the one thing.
there are enough baremetal emulators out there by now that show that you can definitely run emulators without any OS. BMC64, PiStorm/Emu68, just to name a few
Just because emulators often run under an OS doesn't mean that software emulation is inferior to FPGA emulation.
