Whether to rewrite a dying page or redirect it comes down to one question: does the topic still have demand. The two paths salvage different things. A rewrite salvages the topic, a redirect salvages the equity, and reaching for a 301 by reflex because it is the quick fix skips the only check that decides which is right.
Rewrite when the query still has searchers. If people are still looking for what the page covers and it slipped because the content went stale, got thin, or fell behind stronger competitors, then the demand is intact and the page is recoverable. Updating it to match what the query now wants, refreshing the information and deepening the coverage, can win back the rankings on the same URL, because you are repairing a page the audience wants rather than abandoning it. The traffic is reachable, so go and earn it back.
Redirect when the topic is genuinely dead. If the searches have dried up and no rewrite would bring them back, the page has no future, but the signals it accrued, the backlinks and the authority, are worth keeping. A 301 to a relevant page that serves a related need moves that value somewhere it can do work, instead of leaving it stranded on a page that no longer earns. The condition is relevance: the target has to genuinely fit, or you are just building a dead end for users.
So before you choose, check whether the query still has searchers, using search demand data rather than a hunch. If it does, rewrite and keep the page; if it doesn’t, redirect its equity to a page that is still alive, rather than defaulting to the redirect without ever asking.