While I have no experience with the E288CC, I doubt that it would be as good as the 6N6P. The major, and to my mind, critical difference is that the 6N6P and similar tubes require about 750ma to 900ma of heater current. The E288CC requires only 450ma. In general, higher heater current yields higher plate output current.
Given that the 6SN7, with 600ma of heater current, is not up to the task of driving low-Z, inefficient headphones, I would supect that the E288CC would very likely be less "powerful" than a 6SN7.
Apart from the 6N6P family, the only other double triode with a heater current of around 900ma I am aware of is the 5687. However, the 5687 has a different pinout than the 6N6P and thus requires an adapter to reroute the pins.