Both of these methods are about drawing out the final confrontation by running the group through a clock-is-ticking-down activity before they can actually go after the big bad directly.

With challenge immunity, your big bad cannot be affected directly (mentally, physically, or both) until the group beats a challenge (e.g., dismantling the source of its power, figuring out what its weakness is, etc). The big bad, meanwhile, can act freely and may attack them during their efforts, oppose their overcome or create advantage efforts with its defend rolls, assail their free invokes with its own overcomes, or prepare for their eventual breakthrough by creating advantages of its own.

With contest immunity, the group must win a contest to be able to directly attack the big bad—and the big bad gets to attack them while they’re trying. If the big bad wins the contest, it gets to pull off its scheme and get away unscathed.