Hi Joerg,
We moved from Dataverse 3.x to 4.x two years ago, and if you run into questions, you are welcome to contact us. We went through the upgrade steps one at a time. I'm not an expert, but I think that's probably the simplest thing to do, actually. I haven't heard of another way. Most of the effort will be around the step up to 4.x anyway.
We discovered two metadata elements that weren't coming over properly. I see Phil referenced the one about Funding Agency already, so it may have been addressed.
I guess I'm taking this opportunity to flag the other major one for everyone, which is Software name. I always meant to share this, sorry! I lost track of how we fixed it and so didn't have code to submit as a PR. Don't know if it's a known issue or not.
I documented metadata differences between 3.x and 4.x on this gitHub epic (and related sub issues). You'll forgive me if my documentation is a little idiosyncratic and cryptic, but you may find some interest in it if you want to know about things like different note fields. My mapping is in a spreadsheet linked from the issue.
Cheers!
John
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John Huck
Metadata & Cataloguing Librarian
University of Alberta Libraries
5-25E Cameron Library