If you use a sprite when you change the size you can get some pixel smearing/tearing. (So it can look blurry) With the 9-patch (9-slice) the outer border pixels (# set by you) stay the same and the inner pixels are repeated.
Not only does it make the graphic look crisper when scaled it allows you to keep your file size down. So if you just wanted a solid color rectangle you could create a 3px by 3px 9-patch and scale it up to any size in app with no loss in quality, but the server only had to deliver a 3px by 3px image.