Embedded Systems: Is it better in terms of money-making prospects for an electronics engineer to pursue a career doing hardware or writing firmware?

Keep in mind also that hardware development includes writing FPGA systems, so if you're using an HDL, you will still be coding but technically developing hardware.

from my experience it's difficult to get electronics hardware compared to firmware development. both have good scope .you can demand good and reasonable salary in both .But more number of people required for firmware development bcoz it's continuous http://process.My suggestion is follow your passion whether its hardware or firmware development.

Another from experience comment - I think that both of these tasks you describe can be performed in a single job role; its just a matter of finding that job. There are alot of opportunities to make good money in both roles, but I think there is more of a demand in software.  That being said, understanding hardware first and having experience in it will benefit you extensively over the long haul if you move to software.  You will have expertise that many firmware developers may not have which could demonstrate that you are one cut above the rest.

If you can, do both. But this is something that comes with experience. Although firmware (procedural software) isn't all that difficult to master, FPGA's can be a bit difficult. And you need to take extra caution when you design hardware and write HDL for FPGAs. You need to be aware of clock speeds, clock domains, grounding noise, etc. And writing HDL (correctly) can be difficult than (DSP) firmware. You need to alter your thinking for parallel execution and the clock is a very important part of your program (which we tend to ignore when working purely with software).

There's not much money to be made in hardware these days. There is, however, money to be made if you can do both hardware and firmware. You design the board, you write the firmware, you get paid for all of it, and you end up with a better product because you can make tradeoffs between hardware and software that make a product faster and cheaper. That last bit is particularly difficult (read, never happens) when the work is split between hardware and software people.