One of the big advantages is that you can print your expressions using LaTeX:
IPython's notebook allows you to easily publish results. They include all you want and need: latex, imshow and nice code with many languages. But it's not good for generating results.
Perhaps the area it lacks most in is querying variables. In QtConsole, you just type `plot(x)` and see a plot with no side effects. In the notebook on the other hand, you have to type `plot(x)` into a new cell unless you want to rerun your code again and you have to delete that cell later (otherwise you have an unreadable notebook). Plus, the default keybindings (while easy to see) are not intuitive; I don't instinctively know how to jump back a cell.
To select a previous cell just press UP in command mode (or press Esc-UP in any mode). Ref: http://nbviewer.ipython.org/github/ipython/ipython/blob/2.x/...