It is a fair question to ask as you can see in your level administration, you are presented with both options. It also seems that both of these do the same thing. You would be correct to assume this. Both of these perform the exact same function; they classify your organizational levels into groups based on the dimension/attribute assigned to them. In other words, it is a tag. the most common application for both of these is to generate an alternative view of your level structure without having to re-parent or change anything in your existing level structure. However, the uses for attributes/dimensions on levels does not stop at the alternative hierarchies. Attributes and dimensions are used in reporting primarily to group levels in any way you see fit. It is easier to add one element to the report rather than manually picking and choosing organizational levels to add to a report. Attributes/dimensions make it much easier to run either matrix reports or OfficeConnect reports leaving you with less prep time and more analysis time.
But the question still remains, what is the difference? When should you use dimensions and when should you use attributes? The answer is simple: do not use level dimensions and ALWAYS use level attributes for tagging purposes. The reason why you see both in your level management screen is because level dimensions are a legacy function that has been in Adaptive for a long time. Attributes, on the other hand, are a relatively new feature that made its way to Adaptive Insights. As a side note, attributes are also available on accounts and custom dimensions. Another advantage of level attributes is that they are located in their own section in the Model Management screen rather than being lumped in together with regular custom dimensions. This makes appending or updating attributes much easier.
A more technical reason for using attributes over dimensions has to do with how each of these elements queries data for a report. A report with level dimensions would query all of the level dimensions on all levels and then uses suppression to filter out values not pertinent to the report. A report with a lot of level dimensions & organizational levels would perform slower than expected in this case.
Level attributes, on the other hand, only get data for levels on the report and ignore the rest of the levels so that report performance ends up being much faster where a large number of levels is present.
The reason why we still keep both is because level dimensions are a legacy function, and some of our clients still rely on level dimensions to run their reports. As a general best practice, however, we always recommend using level attributes over level dimensions whenever possible.