In that case, I think it'll be wise to mention that in your letter of explanation (LOE). You can attach scans/emails from the Indian High Commission to back up your word.
Difficulty level is the same since both use the same syllabus and format. As for professionalism, I'd recommend British Council. My experience with IDP isn't that good.
As far as I know, they don't recognize Bangladeshi driving license. However, they will let you drive if you have an International Driving Permit. Details: http://www.brta.gov.bd/newsite/en/international-driving-permit/