In what situation would it be advantageous to start a SEP instead of a 401K?

Nothing like an open ended question. Well, a SEP is funded with employER contributions only, and a 401(k) permits employEE deferrals, so here are some that come to mind:

Small business wants to make contributions for its employees, doesn't want to be bothered with processing deferrals, wants to save on admin fees, doesn't care about vesting.

Business wants to make contributions for the prior year but didn't have a plan in place.

One-person side business wants to set up a retirement plan and can maximum 401(k) contributions in another job.