Whether the property is foreclosed or there is a short sale there will be likely be no income from discharge of indebtedness that has to be included in income.
See Questions and Answers on Home Foreclosure and Debt Cancellation
The most common situations when cancellation of debt income is not taxable involve:
When cancellation of debt income is excluded from income there is usually a requirement to reduce tax attributes; so the only minor difference there may be from the two courses of action is the amount of tax attributes to be reduced; but that may not even apply in your case. You will have to discuss all the facts and circumstances with a tax practitioner to be certain there is any difference or not.
Either course of action should result in there being no addition to your income.
It does not matter if is reported to the IRS or not.
I hope this helps.