The potential financial advantage is primarily the use of the house during the pendency of the divorce action, which may have some financial benefit depending on how the bills of the house are split during the separation. There is also the immediate expenses for moving and replacing any furniture or other necessities, but unless one party buys the other out from the house both will eventually have this cost.
There are potential problems with one party controlling the property, for instance they can make it more difficult to show to potential buyers or fail to perform necessary repairs and upkeep. If you believe these are a serious risk, you may want to agree to orders on these issues before leaving the house. A solid written agreement can prevent most of the financial problems that might arise by leaving the home before the divorce is final, or at least provide for mechanisms to compensate one party if there are issues. If you are unsure of what you should do in your situation, you should consult with an attorney to discuss the specifics of your case.