pert:
Sounds like you're bypassing the level shifter on the ESP8266 rx line. You can probably get away with it but since it's already on the shield I'd advise you to use it. Sending 5v signals into the 3.3V ESP8266 might cause damage. There's some disagreement on whether the ESP8266 IO pins are 5v tolerant or not but I say better safe than sorry.
I did try passing the rx and tx from the arduino through a separate level shifter and then on to the ESP, but it would not initialise. The test sketch kept saying no ESP present.
So if the ESP already contains a level shifter then that would explain why the above was happening.
Also would seem to explain why there are 2 x tx and 2 x rx sockets on the ESP-13.
Presumably the one I chose to use has the level shifter associated with it while the other tx/rx set presuably doesn't.