Whether you get an Associates or Bachelors, both degrees take the same licensing exam and thus will have the same job responsiblities.
A bachelors is supposed to make it easier to transition into management; however, most facilities require an advanced degree for management positions, unless you're promoted from within the facility..
A BSN makes you more marketable to hospitals that need to achieve or maintain their magnet status.
There are many political theories about which degree is better for the profession as a whole. If you're interested in that side of things, visit almost any nursing forum and you'll find many and varied discussions on the topic. (www.allnurses.com is a pretty good one.)
As hospitals are pressed to economize more and more, one way they'll do so is to reduce, as much as possible, nursing staff. Nurses are one of the most expensive parts of a hospital. Therefore, when it comes to hiring, they are going to hire the most experienced they can get for the cheapest wages, and barring any experience, they'll hire the most education they can get for the cheapest wages.
If you have the time and the money, I think you should pursue a BSN. If you don't, then an ASN is perfectly acceptable. Most of your education will come from on the job training anyways, and there are a myriad of bridge programs avaible.
-- AngieO'Plasty, BSN