You might want to take a look at my blog here on Trulia, titled short sale vs. foreclosure....I just addressed what the difference was briefly.
The main difference between the two is the impact on your credit score. You should talk to your tax preparer, or attorney as to what may be most beneficial to you.
However....word of advice, if you elect to choose foreclosure...stay in the home as long as possible. I recently had a client contact me that their attorney advised them to file foreclosure and more out immediately. That was 8 months ago, and the foreclosure still has not taken place. They could have still been in the property and saved that money they paid for rent.