The iPhone was eliminated fairly quickly...the portrait-to-landscape flip is easy to circumvent if you do it slow enough or at an odd angle. The Wiimote might be the winner; it registers small, slow movements with ease, as when executing a drop shot in tennis or tapping in a putt in golf.
Newborns, however, are born with something called the Moro reflex. When infants feel themselves fall backwards, they startle and throw their arms out to the sides, as illustrated in this video. Even fast asleep they will do this, often waking up in the process. So while the Wiimote's accelerometer may be more sensitive, the psychological pressure exerted on the parent while lowering a sleeping baby slowly and smoothly enough so as not to wake them with the Moro reflex and thereby squandering 40 minutes of walking-the-baby-to-sleep time is beyond intense and so much greater than any stress one might feel serving for the match in tennis or getting that final strike in bowling.