I'd keep it on the bike, I mean, in the city, when you're flashing joggers and drivers in the face at distances of closer than 20-30ft, it can seriously blind you for a minute or two. At least on the bike, I always have it pointed relatively straight forward, another problem is that if you're looking to the left, WHAM! doored from the right or run over by a car pulling out of a parking spot cause your light was facing the wrong way.
It's also a potential liability. A blinker, they can argue in court that it was lost in the glare of the other lights, and your HID, bright as it may be, they can claim was pointed in the wrong direction cause you were looking the wrong way.
I find it's best when you don't need to "see" around corners, to have the strobe on your head to attract attention where you look and the bright light fixed, like a vehicle. Also, mount it upside down on your bars, the lower angle creates more depth of field and also protects the light in the event of an accident.