yea, having a PC on the bot allows you to use 3rd party software and peripherals (like voice recognition software and webcams) which would be a definite bonus to a project like this.
if you use a PC on board you will still need an extra device interfaced with the PC to control the robot's various actuators.
some sort of microcontroller would be a good option for this although there are off the shelf modules that you could connect to a PC to control your motors and pneumatics.
another option would be to have a microcontroller on board communicating wirelessly with a PC somewhere near by. it's not as elegant a solution though but it does save you from the headache of trying to get a PC to run off batteries.
if you dig around on my robot's website http://mrdunk.googlepages.com/home
you'll see details of my approach (embedded Linux machine connected to a microcontroller network for controlling actuators and reading sensors).
i guess a large part of this will come down to what is your experience with electronics and embedded computing?
ever programmed a microcontroller before?
ever worked with embedded linux?
how much time are you willing to invest? how quickly do you want a solution?