This is a common question among those facing bankruptcy, especially bankruptcy brought on by falling behind on mortgage payments. So what's the right answer?
When dealing with the bank that you have to pay your mortgage to, if you opt for a short sale and they agree, this allows you to sell the house for a value lesser than what you initially paid. If the bank accepts this agreement with you, you will no longer be held responsible for any more mortgage payments on the home (as it is no longer yours as of the date it is sold to the new owner.)
This allows you some breathing room, and while you will no longer own the home, you will have the money that you would have had to use to pay the mortgage to pay for other outstanding bills and/or for rent elsewhere.
The disadvantage is that it's pretty much up to you to find a new buyer for the home, and the bank that you have the loan with will have to agree on the new price of the home. If you're not quite sure what the bank will go for in terms of the price of the home, it can be an uphill battle. That said, most banks will work with you to some degree because getting a mortgage of some kind from someone is better than having the home go into foreclosure, which leaves it up to them to price and sell themselves.
Make sure that you discuss all of your options with your bankruptcy attorney -- short sales are not always the best answer for every consumer, especially given the state that the home is located in. It's always best to know which option best suits you and your chances at a better financial future.