I tried a few times at my work computer, and got results ranging from 45 to 58 wpm. Apparently my keypad and typing speed are actually pretty close. O.O

This does confirm my suspicion that I don't compose significantly faster at the computer as opposed to on my phone. This limiting factor is more the rate at whhich I can decide what to write next and how to phrase it, not so much the speed at which I enter it.