It depends. If you are using the MySensors driver (with NRF24L01+) or the ESP8266. Most MySensors sensors can be powered by batteries that can last for years before you have to replace them. The ESP8266 is much more power demanding. Powering them with batteries is almost impossible.
Last winter did I see if it was possible to build a CNC mill, and it was know I can mill surfaces upp to 1100x800mm. I did also wonder if it was possible to build a vacuum table to the mill, and it was, powered by a vacuum cleaner. This winter did I start to play around with arduinio, and came across of mysensors and this site. I am pretty good at mechanical stuff, but nots so good with eletrical, and really bad at programming.
But it is very interessting stuff, and you can do a lot.
What I would like to learn is combining sketches, cause it seems like a really waste to use one arduino to one sensor. Combining like temp, humidity and relay must be a very good combination.
You're write. The problem is that with a Atmega328 (Pro Mini) you only get 32KB of code, and the nRF24 + mySensor layer take a large part of it. That said, you could monitor the temperature of all the room of your house with a single Pro Mini, if you could put all the DS18B20 on the same 1-wire bus.
With an Atmega2560 you get a lot more flash and it's easy to manage more peripherals (LCD+touch,SDcard,RTC..) actuators and sensors.
Concerning power supply, I think that almost everybody run Mega and ProMini 5V from AC mains and ProMini 3.3V from batteries.
Xavier wrote: You're write. The problem is that with a Atmega328 (Pro Mini) you only get 32KB of code, and the nRF24 + mySensor layer take a large part of it.
I have been playing with standalone 238ps for low power and have noticed that RF24+My sensors is pretty big. Trying to decide if I should connect 2 328ps via I2C or order up some 1284p chips:
I can run them standalone, though not quite as low power because the omniboot bootloader is 16MHz (I can run the 328ps at 8MHz with the internal oscillator). Even at 16 MHz, power draw should be minimal in sleep.
I didn't know about 1284p modules, they seem to be very expensive. Prices for a Mega 2560 board start from 10€ on eBay and 2€ for the ProMini 16MHz.
But maybe you don't use the module and only the chip...