Currently I am using 301 Redirects in my .htacess file to redirect old URLs to new URLs. Are there any performance benefits (i.e. site loading) o using a plugin like Redirection or should I just stick to hardcoded 301 Redirects?
.htaccess catches requests before WordPress is even started. That’s much faster than any plugin.
For a handful of redirects I wouldn’t install a plugin. You need that only in cases when the server cannot know the new address, for example if you rename permalinks (slugs) automatically (you shouldn’t ;)).