BDD is from customers point of view and focuses on excpected behavior of the whole system.
TDD is from developpers point of view and focuses on the implementation of one unit/class/feature. It benefits among others from better architecture (Design for testability, less coupling between modules).
From technical point of view (how to write the "test") they are similar.
I would (from an agile point of view) start with one bdd-userstory and implement it using TDD.