Flashing lights are more visible by a substancial amount.
That little coin cell light could be excellent for riding in a library during a black-out, but on a city street at night, where it has to compete with street lights, neon signs, and the ridiculous HID kits some people put in their cars, how are you going to make yourself stand out? Bicyclists cannot compete with intensity and shear lumens output of competing light sources, and have used motion to visibility, the On /off flashing uniquely visible against a backdrop of constant light sources.
(In my first post, I spoke of jumping the circuit board with a wire to run the led direct from the battery. for the following test you just need to connect the battery directly to the emitter (observe polarity, for 5mm leds, inside the emitter the thick post holding the diode in the center is -'ve, the small little post off to the side is +'ve)
If you're unconviced, lean your bicycle against the side of your car, turn on your constant red bike light. Turn on the car headlights, and walk away. The dim red is quickly overwhelmed by the brighter white headlights. Sure, the red could be seen if you looked for it, but the issue many of us cyclists have is that motorvehicle drivers are oblivious to cylcing even at the best of times. If you put a flashing red light next to your car headlights and walk away, the flashing is a dramatic visual prompt - hopefully every motorist ever behind you is attentive enough to pair the flashing light with respect for you as a cyclist.
IMHO the absolute best way to earn respect and protection from automobiles is to make yourself very visible, visible for hundreds of feet. If you make it very easy for drivers to see you, to konw where you are going and understand clearly the path you would like to take, you will often find them being very accomodating. I often feel drivers appreciate the effort I spend in making myself known to them, I often feel like they indicate their gratitude by the clearance they leave me.
What I'm saying is, put some good lights on there: a hundred or a few lumen at the front AND a front white flasher (helmet level is best) and a bright red flasher at the back AND a red flasher on helmet rear (almost eye-level for most suv/pickup truck drivers)