Recently went through this non-hypothetically, although there was an additional factor involved: My advisor was paying for relocation costs "within reason". Obviously, relocation costs don't cover "toss/sell and buy again." So, we shipped by UBox.
We kept my futon, my desk, bf's dresser and kitchen table, a cubey shelving unit, and both our extensive collections of kitchen appliances and glassware, though they may not have been worth the $1k it took to move them (actually, altogether, probably was. Roughly.). We left both our twin beds, I left my dresser (thought it would sell well with matching bed, ended up selling to girl who took over my lease). I gave away to friends or Goodwill a bunch of clothes and random household goods (wine rack, fan, space heater, etc). He left his nondescript Target bookcase to his roommates. Upon arrival we bought a mattress/bed, thrifted an awesome coffee table and nightstand, and bought new shelves and chairs when we couldn't find any we could tolerate at thrift stores/CL.
In retrospect, I'd be willing to spend $1-2k out of pocket transporting the things I genuinely like long-distance, mainly to avoid the hassle or expense (pick one) of re-acquiring similar things. But I do also see moves as a great time to purge the things we keep "just in case," that we don't actually care about much.