Verifiable delay functions vs Proof of Sequential Work
A typical thing which you cannot do with a proof of sequential work is achieving time-lock encryption. In time lock encryption, you want the user to be able to retrieve the hidden message only after some time (i.e., you want to "send a message to the future", as its inventors initially put it). With a VDF, you can use the unique secret to mask the secret message $m$ which you want to send to the future; with a proof of sequential work, there is no clear way of masking a message such that retrieving it requires solving the puzzle (except in an interactive way, where another party checks the proof of sequential work and send $m$ if the check passes).

See also the discussion page 23 of this paper: proofs of sequential work fail to replace timed commitments in protocols that seek to achieve fairness. I believe that VDFs, on the other hand, can be used here, since they do not suffer from the limitation that prevents proofs of sequential work to be usable here - namely, that one can lie to the verifier about what was the solution to the puzzle we solved, even though one must still invest a given amount of sequential work to solve the puzzle in the first place. With VDFs, you cannot lie this way.