Both InDesign and Publishers are excellent design tools and have their own capabilities and strengths suitable for different design needs.
Publisher is designed for normal MS Word users who also want design capabilities. It is only available for Windows (PCs) and is more suitable for printed products, such as flyers and brochures, which may be printed with laser or InkJet printers.
InDesign is a more sophisticated product known for precision in layouts and numerous output formats. If you need primarily digital assets and advanced capabilities, you will choose InDesign.