Floor addition plus dig out comparison

[Alazar Wubet]

I'm flipping this house in Washington D.C and needed an extra bedroom. The two options were digging out the basement and adding a bedroom there or adding an additional floor and putting the bedroom there and leaving the basement as a living space. 

from bids i received i realised it'll cost almost equal for both but i can't find an answer if the permitting process would be lengthy for the addition. 

which way do you recommend i go?