Difference between EEWB and BDT 

BDT, among other things, is used to add/delete/disable fields in the BP transaction only. It does not create new objects for the developer to play with. BDT as a separate unit in CRM (TCode BUPT) has several useful tools like BP events which are useful at times.

Whereas EEW can extend several transactions in CRM including BP and it extends the business object by creating several z-objects like an active BADi implementation, middleware objects like z-function modules which you can use for coding your custom logic.

But there's a lot in common for BDT and EEW - they both create the field groups, views, sections and screens when you enhance an object. You can use BDT to change titles such as tab name or section name after you have created the easy enhancement project for a particular object!