To move specific line  (Current, locals, arguments...) from a grid to another inside the objects tool panel, you need to click on the [v] black triangle pointing down in the tool's title toolbar.
This will popup a menu with 
  Object tool: left -> ...
  Object tool: right -> ...
Using the "right" you can select, for instance, "Current Object" and "Dropped References", to have the same layout as previous EiffelStudio's releases.

To be able to choose the order of the entries, this is in progress and should be available for 6.0 .