Arduino nano to esp8266 level shifting needed?
The arduino nano v3's logic is 5v, and the ESP8266's logic is 3.3V, so you need to do level shifting between both.
Using a voltage divider drains more current (guess not an issue in this case) and it's ok only when going from 5V to 3.3V (when the signal must be shifted from 3.3V to 5V in the links you provide, it looks like it's based on that 3.3V is still considered "HIGH" on a TTL signal). 

I personally prefer using a level shifter, it just complicates a bit the Bill Of Materials, but you won't have to debug the level shifting part.

And better than that, using an arduino mini pro @3.3v working directly at 3.3V gets rid of this hassle.