Unlike the W-2, a 1099 is not included when you file with your 1040 personal income tax. It is primarily for informational purposes - you use it to calculate other amounts. A copy is also supplied to the IRS, so you do want to ensure that your social security number is correct. Other than that, the address isn't really relevant - except as noted above that there could be issues with earnings in different taxing jurisdictions (different states may have different income tax rates, for instance, or it just may change your total in a given jurisdiction).
The address is rarely important on any of the forms (except regarding your actual address to send a refund) - you might move several times during a year or even between the first of the year and when you get your forms, or when you file. You could also have different mailing addresses (a P.O. Box, a work address, etc.) that would appear, which would not necessarily reflect your home address at any point in time.
You should follow up with your bank anyway to ensure the correct information is carried through their system - they may have different mailing address and physical address entries and only one got updated.