It really depends on the type of banner you are going for. Will it be a full-color printed banner, or are you getting a vinyl banner in a one or more single colors?
Illustrator works really well if you're just looking to make something simple or need specific logos or designs that are vectored, but if it's something more artistic that will require a lot of layering and management of images and photos, then InDesign would work.
Big question is will your artwork need to be cut out using a vinyl plotter (outlined vector art only) or printed on banner material using dyes or some kind of ink-like process (bitmaps would be OK at high resolution)? That's going to quickly determine which way to go.