Newer versions have newer features, more bug fixes and longer support cycles.
Obviously, they also introduce new bugs. But, if in doubt, I would always recommend upgading to the latest stable version. This is now 4.4. There's no point considering 4.1LTS as this runs out of support at the same time as 4.4.
3.11 is no longer supported for bugs or security fixes so isn't a good place to be.
There's no such thing as Moodle "4.x". Each version of Moodle has its own upgrade requirements. One of those will be a limit on how old the version you are upgrading *from* can be...
4.0 is 3.6
4.1 is 3.9
4.2 is 3.11.8
4.3 is 3.11.8
4.4 is 4.1.2