What is the most efficient (ie. less server intensive) way for 301 redirects?

.htaccess allow you to perform the redirection without the need of any single line of PHP. Using WordPress to do redirections means that WordPress engine is loaded, then the user is redirected and WordPress is loaded again in the new location. So, as general rule, .htaccess redirections requires less servers resources. If you don’t need interaction with WordPress to know when and where to do the redirection, use .htaccess.