In my opinion, the EF objects would be mapped to yours. This has a higher development cost, but gives the added benefit of persistence ignorance and decoupling. This decoupling can translate to significant agility and real world savings in the long-run, should the business need to switch to a different persistence solution. Without the decoupling, the EF objects can become deeply embedded in the BLL and even presentation layers, requiring a huge refactoring. In such a case, the business might not even consider switching persistence solutions, which could cause the business to be less competitive.
The decision to reap this benefit at the higher development cost depends on the amount of risk the business is willing to take. I suggest you consult with the project commissioners and use your best judgement to interpret their strategic objectives in a technical way.