The main difference between these two methods is that if you choose Edit > InCopy > Export, you will generate an external file that needs to be saved in a separate location and can be used in an InCopy workflow. The Place and Link method achieves a similar result in that it appears in the Links panel however there is no external file (not that the user can access anyway). Unless you are using an InDesign/InCopy workflow, there's no need to use that method as this is now built in to InDesign using the Place and Link function and also by using the Content Collector/Content Dropper tools. Place and Link would be the best option in this case.
InCopy is an external application.
This method is handy if you're going to using InCopy files to hand off to an editor to put through final text changes. They see the layout and make the corrections accordingly but will be restricted to the layout setout by the designer.
It's also handy for using over multiple documents
Other uses of InCopy http://indesignsecrets.com/add-pdf-comments-indesign.php
Place Linked Text
This just creates a link to the original text within the same document.
I use it for the cover of a book where the name of the book appears on the spine.
that means as years go on I just have to change one area of the file to update the rest of the areas, like a spine area.
There are other ways
I need to be able to unlink text to create different versions of the documents. I need to create new versions of the indesign document every year but at the same time I need to keep the old version. My solution is to take a copy of the indesign file to create the new version. In the old file I remove all links to keep the older version.
With InCopy this works by unlink the text or cancel an assignment package. In Assignmnets panel I select all text and choose Unlink content.
Can I do similar with a the Place and link-function? When I delete links in the Links panel the link and text disappear.
Is it better to use the Incopy-function when I need to be able to create different versions?
Actually based on what you are describing, the place and link feature might be a better choice for you. The links created using place and link are specific to that document unless of course you place and link to/from another document. There are no external files to deal with using place and link. So if you are creating these links within a single document, you can do a "save as" and those links will carry over to the new document, no unlinking required. That being said, unlinking is easy to do when using the place and link method. Simply select the "child" text and go to the links panel and choose unlink.
Now if you are using the InCopy stories now to allow InCopy users to edit the text, then you should probably stick with the InCopy method. In cases like that, you're comparing apples and oranges as the place and link will not allow InCopy users to edit that content.