What is the difference between exposing the agreegate properties like page, pagelist and pagegroup through the declare index and use them in reporting whenever needed and achieving the same through concrete classes?

I understand the db size might be increased if we go with declare index concept as the data gets stored in both blob and index tables, apart from that what are the other differences. I also understand that it is the best practice to create the data model way before, but during the case implementation or during the sprints we don't want to change the existing data model. At that time declare index might be the option .

My doubt is when do we go for declare index and when should we for the data type (external storage) ?

I do agree that we need to save the reference data in the data types, but what could be the difference if we achieve the same through declare indexes?