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"
We are excited to announce the open beta program for self-hosted runners. Bitbucket Pipelines Runners is available to everyone. Please try it and let us know your feedback. If you have any issue...
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