Thanks for the links, I had a little look through them. Unfortunately, there's not a lot of common attributes between these 2 shapefiles to get a decent enough result. For example, simply using the JOINS option on the name columns
SA2_NAME11 would only give you ~67 fields in the attributes table.
Personally, I would spatially join the layers by using functions such as the Join attributes by location.
Vector > Data Management Tools > Join attributes by location
SA2_NAME11 as the Target Vector will produce an attribute table with the layer's original attributes plus any attributes of
CEO_CODE13 when there's an overlap. And vice-versa when you switch the layers and run the same function.
However, since we're doing a spatial analysis and there's a slight misalignment in some areas between the 2 layers (as your image shows), you may see incorrect attributes in certain parts. You could manually rectify the incorrect attributes if there's only a small handful.
One of your images also shows calculating a ratio and percentage value, however, the only numerical data provided (excluding the codes) is the area size. Are you wanting to calculate with the ratio/percentage with the area size?