You will need to stand up a new Jira server, ideally of the very latest version of Jira server, get a licence for it, then export from Cloud and import into the Server version.
See https://confluence.atlassian.com/adminjiracloud/migrating-from-jira-cloud-to-server-776636236.html for a good overview and more links. Pay especial attention to the "system admin" account - people seem to miss that a lot when moving off Cloud.
"Better" is a matter of your needs and opinion. I can answer it for specific subjects (e.g. "flexibility" - Server wins because I can customise and code what I like), or if I have specific information about roughly how you want to use it and what for, it's impossible to say "better"
For JSM June Challenge #2, share how your non-technical teams like HR, legal, marketing, finance, and beyond started using Jira Service Management! Tell us: Did they ask to start using it or...
Connect with like-minded Atlassian users at free events near you!Find an event
Connect with like-minded Atlassian users at free events near you!
Unfortunately there are no Community Events near you at the moment.Host an event
You're one step closer to meeting fellow Atlassian users at your local event. Learn more about Community Events