You mean HTTP vs. MQTT? I don’t think that there is any difference between the two in terms of power consumption. Both need a running wifi connection along with an IP stack - so basically, the processor is running most of the time.
I have my sensors connected to mains power all the time - I did a quick check and found that they are using 2W of power each. The main source of power loss seems to be the power supply itself. I had a bunch of old 3V3 wall-wart power supplies sitting on my desk and put them to use, no special consideration here.
But @mjptec mentioned in this thread that he wanted to investigate operating the sensors from a battery. The main power draw occurs when wifi is switched on, but in deepsleep mode, the ESP8266 draws only around 20 microamps. I therefore think it is a viable option to have the ESP8266 powered down most of the time and then wake up just to take a measurement and submit it to OpenHAB.