If you need a Jenkins installation that starts easily, runs easily, and upgrades easily, and don't care as much about being able to repeatably create that exact same installation and all its configuration on another machine, use the package installer, especially the Linux package installers (CentOS, Debian, Red Hat, Ubuntu). You can use Jenkins configuration as code to configure this just as any of the others, but don't add the complexity of managing a Docker image.
If you need a Jenkins installation that you can consistently create the same installation on different machines, then choose a Docker based installation. Docker installations use the war file and allow you to specify your custom additions.
If you have a platform that does not provide a package installer, then use the war file.