The Cateye Doubleshot has a brighter spot (intended as the helmet mount light of the combo) and the Triple puts out more light, but as a wide flood so does not seem as bright.
So if you ride in pitch black like forest trails, then I prefer lights like the double on my helmet to let me scan the terrain, but in more developed areas, the flood may suit you better. The double is also preferred by a couple of road riders I know because from the handlebar it focuses a long beam of light on the road and allows them to ride at speed when out on country roads (we have reduced winter daylight here at the moment)
Actually, both together would make an excellent combo, but my girlfriend would have to agree to a rasie in my 'allowance'.