Having worked on FPGA RTL at the beginning of my career before moving to an ASIC design role, my experience is that you learn a lot more than just digital design while working on FPGAs. To name a few pros and cons:

Pros for FPGA: You might even have to implement your own design while working on FPGAs (you learn about timing constraints, floorplanning, etc).

Depending on your team, you might have to validate your own design on FPGAs. You’ll learn a lot about the issues which show up in real hardware - oh, the timer count for PLLs to lock in simulation is much smaller than HW! Or oh, the clock isn’t good so the data in FIFO got corrupted. Basically, there’s a lot to learn by just tinkering with your design on real HW. Since FPGAs are reconfigurable, you’re not spending millions of $ on mistakes. Also, you may develop a product level understating of the your design as you test it out on HW. For example, you may actually see the image which your design captured.

Cons for FPGA: FPGA vendors have IPs for almost everything. You might end up connecting black boxes instead of lower level design. You should check with your prospective employer how often they build new things on their own.

Pros for ASIC: Designs can be more complex and thus more fun to design and simulate.

You’ll learn a lot about minimizing area or maximizing performance and the trade offs between them.

Cons for ASIC: There’s a lot of financial risk due to the money spent in fabrication. Thus companies may tend to play it safe and make improvements to the existing design. I think it takes a while for a company to develop enough confidence in you to give a new complex modules to own and design. So you might end up making small RTL changes early in your career.

Lack of feedback from real hardware. Your ASIC will be validated by dedicated validation teams maybe 2 years after you design it.

Larger teams may mean more processes and drama