If you already have some FPGA experience, I'd say build on that if you can.
Absolutely anyone in this business can pick up a small microcontroller and make it do stuff. It's a commodity skill, and anyone else applying for the same job as you will be able to do it too.
If you're confident programming FPGAs, though, then that will mark you out as having a special, worthwhile skill. Have a read around the forum; there are precious few FPGA threads, and those there are tend to be from people just starting out, learning the languages, and struggling to figure out how to make them tick. There's little (if any) more advanced discussion, and few people who are able to confidently answer questions about them.
For about the last 15 years or so, I've been designing products that combine a general purpose processor of some kind, with a programmable device. The CPU runs the application code, and the FPGA or CPLD does the thing that's interesting, unique, and really hard to do any other way. Whether it's implementing an unusual serial protocol, supporting a great many channels of <insert interface type here>, or driving external circuits in a complex but time critical way, the FPGA is the part which makes it possible.
Be the person who brings FPGA know-how into a company, and you'll be a valuable asset.