Your LinkedIn profile is public, and your contacts might notice if you padded it conspicuously. Even more important, it’s _one_ thing, whereas a targeted résumé is what the target wants to hear.

When reviewing résumés for a software quality assurance position in a trendy sector, I saw numerous résumés from people with no apparent desire to do software quality assurance, but plenty of desire to move into the trendy sector. One was from a senior manager, who had sometimes supervised departments that included lots of stuff, including QA. His targeted résumé differed from his public profile basically by appending “& QA” in several places. After that, I largely ignored targeted résumés.

That's not the point. Resumes work today, but LI could work much better tomorrow.