My 2003 325xi automatic headlights worked pretty well. The sensor seems to react more solar radiation rather than visible light. Usually the headlights came on well before sunset in the winter and during the summer almost right at sunset.
My X3 does appear to be even more sensitive. I wish we could adjust that sensitivity to our liking. I have not seen my headlights on in the middle of the day though. That sounds like a sensor problem.
2013 X3 28i (prem, tech, cold1&2, conv, hud)