The web has blacker blacks and brighter colors.
Print layouts are superior because the position doesn't change and the resolution is superior. Web pages change from one browser to the next or based on the screen width. In print, you know exactly what the final output will look like, on the web you hope for the best.
Pages are generally a common size. On the web, the “page” is often tall and skinny by comparison; the user is expected to scroll.
The web has a slight win with gradients, hairline rules, and pixel perfect images.
It is now expected that web pages have rollover buttons and other subtle animation. Video, audio, mouse effects, text effects, and animation are other examples of interactivity.
There is not much interactivity in the print world, other than the wonderful pop-up books. :-)
Typography is poor on the web. There are licensing issues with using non-standard computer typefaces and if you do find a free typeface, then your page will load slower because the font must be downloaded. Tracking, kerning, leading, etc. is difficult or impossible.
Line, shape, color, balance, texture, contrast, flow, affordances, the gestalt... What ultimately makes a good web designer is the same thing that ultimately makes a good print designer: fundamentals. You just need to know what looks good and what looks bad and have the time and patience to get to good. Knowing your tools helps, and definitely makes you faster, but are just a tiny fraction of what makes a good designer.
Both Graphic Designers (print) and Web Designers (internet) must be able to understand the clients needs and turn it into good communication. Ultimately, designers are responsible for communicating a message.