I've let them work in parallel for few days and the winner is ..... BMP180.
This is a graph for BMP180.
This is a graph for DHT22.
As you can see the DHT22 had few unwanted spikes which leads to false triggers.
DHT22 has the advantage of using one pin, BMP180 is i2c so is using 2 pins, but the temperature has no spikes.
- are reading the same temperature
- both are showing a lower value as my current chronothermostat which is responding more quickly on changing the temperature.
If you know other sensors that are more precise and are more temperature responsive, please let me know.