You keep asking if one power source is better than 2 separate ones or viceversa. As everybody tells you, it depends on what are you powering.
Motors and sometime even sensors introduce power noise and make measurements difficult. Thats why you add those 0.1uF (100nF) capacitors to every integrated circuit in your schematic, to filter out the noise. Also motors drop the battery voltage when they start or change directions, so you need a big capacitor in paralel with the battery to help reduce the voltage drop. And for the same reason, you need to use 10uF capacitors in paralel with every integrated circuit in your schematic, as a power drop dampener. Think about it like the power from the battery is a big beer brewer, the beer pours into a keg (the 1000uF capacitor) that will fill up every persons cup (the 10uF capacitor). So even if the big guy next to you is draining the keg really fast, you still have some beer in the cup to drink until the keg is filled up again. The 0.1uF capacitor might be a paper towel to clear the spils from pouring.
If you need a clean power line for the electronics, having a separate battery makes a lot of sense. But it is difficult to recharge, you need 2 separate chargers, or, if you use the same voltage for both batteries, you need to charge them separately, since they will discharge differently. For a small bot this is ok, but for a big robot butler that will self recharge it is anoying. But anyway, a small bot will most likely work (if you do a proper filtering) with a single power source. The only time I see a benefit having separate power sources is when the bot uses motors with double or more voltage difference. 12V DC motors for driving and 6V servos for the head and arms. Even in this case, if you use a switching voltage regulator like in Admin's schematic for the servos, you can go ahead and use a single power source for the whole robot.