At the end of the page, it’s written “We use 10 kΩ resistors for mains powered monitors. The emonTx uses 470 kΩ resistors to keep the power consumption to a minimum, as it is intended to run on batteries for several months.”

Why then not using always 470k for R1 and R2 ?!? are they any other drawbacks ?!?

As long as the decoupling capacitor is able to supply enough charge for the multiplexer to transfer to the sample-and-hold capacitor without the voltage dipping too much, the resistor value has little effect in normal operation. Where it does have an effect is at power-up, when a lower value means that the bias reaches its stable operating point earlier.