It's two sets of phonetic symbols and one set of ideograms.

In my experience, the speed difference between Japanese and English on a phone keypad isn't substantial, assuming you have a modern phone that will "guess" which English word you mean as you're punching the buttons. On my cheapie Japanese phone, which didn't have that function, it was much faster to type messages in Japanese than in English (so much that I would routinely write to American friends in Japanese, just to save time). But that phone also had a sort of "guessing" function for Japanese words: if I started a word with "ro," one keypress later would complete the phrase "Roppongi Hills."

In the end, speed is more a funcion of technology than a function of language.