THe GPIO is not going to help you build a custom H-bridge to drive motors forward and backward with variable speed. You can use the 2 relay switches to make one of those, but it will be noisy and you only get 1 H-bridge out of all that wiring. You can get an add-on board for the Pi but most designs (I have seen) seem to hijack all the GPIO pins, so any sensors you want to add onto your robot will likely have to use USB (which rules out a lot of the cool low power stuff).

There is a place for both systems, they do different things (even though there is some overlap) so for any moderate project (say a little hexapod robot) you are likely to use both. The Pi as a general purpose computer that can do all your nav/ANN/signalling stuff and an Arduino board to receive the signals and actually run your motors/servos (assuming you need more than 1 or 2).

They overlap, but are quite different. Arduino is a high end microcontroller, Pi is low end computer. If you want real time and low power, you want to be on the microcontroller side of that divide.