Improve the content first when a page has stalled because it does not fully satisfy intent, and build links first only when the content is genuinely strong yet outgunned on authority. The split that matters is the diagnosis: is this a relevance problem or an authority problem? A page can stall for either reason, and the two need opposite spending. Pour links into a relevance problem and you have funded a page that still does not answer the query, which is money lit on fire.
Most stalled pages are relevance problems wearing an authority costume. The page covers the topic loosely, misses the sub-questions the searcher actually has, or repeats what every competitor already says without adding anything new. Links cannot fix that, because no amount of authority makes a page more responsive to intent it never met. The tell is in the comparison: read the pages ranking above yours and see whether they answer something yours does not, or carry information gain, depth, or an angle yours lacks. If they do, the fix is the content, and improving it is where the next hour belongs.
An authority problem looks different. Here the page already satisfies intent as well as or better than the pages above it, covers the sub-questions, offers something the others do not, and still cannot climb. When the content genuinely holds its own and the only visible difference is that competitors are backed by more trust and stronger link profiles, then links are the missing input, and building relevant ones is the move that can finally move it. This is the narrow case the link-first reflex assumes is everywhere, when it is actually the exception.
So before you choose where to spend, diagnose. Put your stalled page beside the ones beating it and ask whether you are losing on what the page says or on who is vouching for it. If you are losing on substance, rewrite for intent and information gain first. If you genuinely match them on substance and lose only on authority, then build links.