Rewrite the near-miss page when it has equity worth inheriting, and build new only when its foundation is fundamentally wrong. The pivot is inherit-the-equity versus wrong-foundation, and it usually points toward the rewrite, because a page that already ranks on page two has accumulated things a blank URL has not. Equity here means real assets: some accrued authority, backlinks pointing at the URL, a ranking history that tells search engines the page is established and roughly relevant. A rewrite keeps all of that and improves the part that fell short, so it tends to reach its target position faster than starting from zero.
The instinct to start fresh because a clean page feels tidier is the trap. A new URL throws away every bit of that earned standing and begins again at the back of the line, where it has to be discovered, evaluated, and slowly trusted before it can compete. For a page that was already close, that is trading a head start for a clean slate, which is rarely a good deal. The near-miss was near for a reason, and most of that reason is worth keeping.
Building new is the right call when the existing page’s foundation is wrong rather than merely weak. If it targets the wrong intent, is structured around a different query than the one you now want, or is built so badly that fixing it would mean replacing everything anyway, then the equity is attached to the wrong thing and inheriting it does not help. In that case a purpose-built page aimed at the correct intent can outrun a rewrite that is forever fighting its own bad bones, even with the slow start.
So look at what the near-miss page actually has before you decide. If it carries authority, links, or ranking history and its core intent and structure are right, rewrite it and inherit the equity. If the intent or structure is fundamentally wrong, accept the slower start and build a new page on the right foundation.