Courtosey of : http://www.dejai.com/dejai%20internet/broadband%20 simplified/dsl_faqs.htm ISDN is a digital service supporting speeds of 64K and 128K in its basic configuration. Broadband is many times faster than ISDN, and for most Internet-related applications, broadband is a better choice. Broadband is also significantly cheaper than ISDN.
In case you were deliberating between getting ISDN or broadband at home consider that you get charged for each 64k channel on ISDN. So, to get the full 128k bandwidth you are charged for 2x telephone calls which turns out to be quite expensive (reiterating Metaphysical's statement that home broadband (ADSL/cable modem) is cheaper).
The main difference is speed and connection. ISDN is slower (64k) and requires you to 'dial up' each time you want to connect to an ISP. Broadband is an always on connection (normally at 512k). There is also ADSL which is similar to Broadband but requires less kit. The service you choose may be determined by what is available in your area.