Your credit score will suffer a more substantial hit by undergoing  foreclosure or giving a deed-in-lieu of foreclosure than with a short sale.

Under a short sale, the borrower negotiates with the lender and the short sale process is completed in accordance between the two parties. 

Experts agree that a short sale may result in a loss of about 100 points on the borrowers FICO score. On the other hand, a foreclosure or deed-in-lieu of foreclosure could result in a loss of in the area of 250 points of more.