To use an Xbee module with an Arduino, you would not need to use an Xbee shield, although it makes the connections easier. As long as you make the necessary connections, you can use the boards together. As far as using the Xbee module with a Zumo, you are right that there is not room for all of the boards together in the intended configurations. It is possible to use them together; although, it requires quite a bit of modification. You can see an example of a Zumo being used with an Xbee module in this YouTube video:
To answer your question about how the Zumo and 3pi compare to each other, both robots can be used to do tasks like maze solving and line following and both have different strengths and focuses. The 3pi has an LCD screen, built-in line sensors, and 3 user pushbuttons. The Zumo uses an Arduino, has an optional line sensor array, and a built-in accelerometer, gyro, and compass. Both robots have a few extra unused pins that can be used to add external sensors. I suggest reading the 3pi Robot and Zumo Robot product pages for more information.
By the way, since it sounds like you are interested in the Xbee module, you might also be interested in our m3pi Expansion Kit for the 3pi Robot, which offers a convenient way to connect additional devices (such as an mbed development board, Xbee, or Wixel) to a 3pi.