As per SSA office, it appears it is better if you take SSN based on EAD.
Check this site:
http://www.socialsecurity.gov/pubs/10002.html
Especially the following question.
Are there different types of cards?
We issue three types of Social Security cards. All cards show your name and Social Security number.
* The first type of card shows your name and Social Security number and lets you work without restriction. We issue it to:
o U.S. citizens; and
o People lawfully admitted to the United States on a permanent basis.
* The second type of card shows your name and number and notes, “VALID FOR WORK ONLY WITH DHS AUTHORIZATION.” We issue this type of card to people lawfully admitted to the United States on a temporary basis who have DHS authorization to work.
* The third type of card shows your name and number and notes, “NOT VALID FOR EMPLOYMENT.” We issue it to people from other countries:
* Who are lawfully admitted to the United States without work authorization from DHS, but with a valid nonwork reason for needing a Social Security number; or
* Who need a number because of a federal law requiring a Social Security number to get a benefit or service.