From what my friend has told me cell phone coverage is pretty good on all NCLA ships when they are cruising and in port, with the exception of a few areas. And I'm pretty sure there are "hot spots" on the ship where you can use Wi-fi for free, but they might be hard to get below decks. I am 100% sure that there are "hot spots" in most, if not all of the ports, so that is always an option.
I just bought a laptop because there are a lot of other uses besides keeping in touch with people that it is going to be good for (movies, music, games, etc.). I'm still taking my cell phone, but if I had to choose I'd go with a laptop. And you will probably want to look into an external hard-drive to bring a lot of entertainment with you.