So you are asking about using new diagramming technology in your Swing application, yes? I assume you are not asking about porting your app to the web. Although my answer will give you the flexibility to consider it in the future.
The functionality and API style of JGo is similar to GoJS when looking from very far away. So although conceptually you will see many similarities, the details are quite different. Furthermore we have had a lot of experience designing and implementing diagramming APIs for various platforms, so you will find that GoJS is a much more mature design than JGo. It is easier to do much more in GoJS with less programming effort than to do the same thing in JGo.
That leads to another big difference: JGo is a document-view architecture whereas GoJS is a model-view architecture. That means using templates and data binding.
So there are no translation tools. Sorry. On the other hand, I think once you are familiar with GoJS you will enjoy the freedom that comes from re-designing and re-implementing your old design and implementation. Another advantage of GoJS is that there are a lot more samples. Almost any kind of node or link that you want is relatively easy to implement either by adapting existing samples or by composing from scratch.
Anyway, I recommend reading https://gojs.net/learn and all of the pages of the Introduction that discuss features that you want to implement in your new web app diagram, starting at https://gojs.net/intro. And if you have any questions, we’re happy to provide suggestions and maybe give you some sample code.