To me I always prefer having a clean install and migrate everything over, this way there's a fresh start of packages and not have to worry about running into any issues for an upgrade and is the method I generally use and preferred.
Now there's nothing wrong with doing a dist-upgrade but if you're going to do that make sure you have a good backup and/or snapshot because if someone goes wrong it'll go wrong fast.
But it basically comes down to what you want to do. The fast and simple method would be to do a dist-upgrade (and hope nothing breaks during the progress but let's be honest, it's Linux, the chances of something happening is pretty slim unless there's that one sneaky package that isn't supported on the newer version that throws a whole ranch in the process) while the slow progress is deploying a new server with the updated OS and doing the migration but more reliable and gives you a fresher start. Personal preferences, and everyone will have different opinions.