For this decision, a targeted improvement keeps the site's overall structure and changes one part of it: a page, a form, sometimes a single shared template. A redesign reworks a large share of what the pages have in common, such as the menu, the page templates, the way content is organized and often the message the site is built around. It doesn't have to replace all of it.
That difference tells you which one a problem calls for. If the problem lives on one page, fix the page. If it lives in something many pages share, each page-level fix has to work around the same limit, and the larger project starts to make sense.
A change in the business is the clearest case for the larger project. Suppose a site was built to sell one product to small companies, and the company now sells three products to larger ones. The menu, the homepage and the page layouts were organized around the old offer. The team can rewrite individual pages, but visitors still arrive at a structure that describes the company as it used to be.
A site that's slow to change is another case. If every new page needs a developer, edits wait on developer time, and the site can fall behind what the business sells. Reworking the templates so the team can make routine changes itself is one reason to take on a larger project.
The last case is a set of task failures with one cause. Suppose testing shows that visitors struggle to find pricing and to tell which product fits them. If both problems trace back to how the site is organized, reorganizing it once makes more sense than patching each page.