job offers choosing
Before I say more, these are my thoughts, and may or may not be the conventional widom.
Yes Broader range of work,move around in different areas of ASIC design, like frontend design, verification, backend, emulation before you settle on any one of these.
Learn about different techonologies, like ASICs in computer system, in mobile space, in embedded applications... the list goes on.. you can go to depth as your interest grows, but definitely one should have an idea...