The only significant advantage of dial-up was that, until recently, it was cheaper. Many broadband packages are now as cheap, if not cheaper than dial-up.
Dial-up services don't usually have limits on the amount that you can download, whereas some broadband packages do. However, unless you're using dial-up 24 hours per day, you can't be downloading anywhere near the limits of most broadband services.
Broadband offers much faster internet access. It also allows you, if you so choose (i.e. you leave your PC switched on and connected to the net) to be 'online' 24 hours per day. That's because you can make and receive phone calls at the same time as browsing the web, sending e-mails or downloading files.
The faster speeds offered by broadband make services such as watching TV online, or downloading full-length movies, possible. (However you need to be aware that such services contribute significantly toward any limits on the amount of data that you can download without paying extra charges).
Chris