Kalvin: In this particular application, the microcontroller will remain in active mode for long periods of time (hours), as it is operating as a white noise generator.
Sure, but you will be processing the signal as discrete samples ie. you will be outputting the noise signal only at specified sample rate. For example, you will be having a periodic timer running at some sample rate, let's say like 48 kHz or 32 kHz. Each time the timer expires it will produce an interrupt. As this application is very simple one, you can perform all processing in this interrupt routine. In the interrupt routine you need to output one noise sample and perform some computation for the next noise sample value [in order to minimize the jitter]. When the processor returns from the interrupt routine, the processor will enter very low power sleep mode consuming only 1 uA - 2 uA. Thus, it is a matter of energy efficiency vs. current consumption. Of course, you can select a small microcontroller with low current consumption, but it may not be optimal solution energy-wise.
You can calculate a duty cycle for your microcontroller affecting the energy consumption: Let's assume that you are running at sample rate of 32 kHz, so the time between each sample is 31.25 us.
1. Lets assume that your little 8-bit controller is consuming 100 uA and it manages just compute the next sample in this 31.25 us. Thus, your duty cycle is close to 100% and your noise generator is obviously consuming 100 uA as the 8-bit microcontroller is busy processing the samples.
2. Next, you want to evaluate a 32-bit controller consuming 500 uA when it is active, and 1uA when it is the sleep mode, but you find out that it takes only 5 us to compute each sample. So, your duty cycle is 5:31.25 = 0.16, thus effectively your 32-bit microcontroller is consuming 1 uA + (500uA * 0.16) = 1 uA + 80 uA = 81 uA.
From this simplified example you can see that a 32-bit controller may be 20% more energy-efficient than a smaller 8-bit microcontroller, although the 32-bit microcontroller consumes 5 times more power when it is in active state.