Builder allows you to move a content entry between models by clicking in the upper right corner of the content entry on the three dots and selecting Move. However, the model you are moving the content from must match the model you are moving the content entry to. In other words, you need to make sure that all the fields as shown on the model’s page match for both models:
In this case both the model I am moving the content from and the model I am moving the content to must have the fields newField and anotherField.
If both models do not have the same fields but you need to move content between models, you can use the upload/download JSON content approach as outlined in this forum post. This technique does not require the source and destination models to match.