I'm not entirely sure what you mean.
The Cygolite 360 that I have is the "360 Lumen" version. There are stronger ones, but they may suffer from some of the problems to which you allude. In online reviews, the 360 is regarded as a reasonable "middle ground" between good lighting vs being too bright.
Additionally, there are 6 modes on these kinds of lights: low, high, medium, "Steadyflash", "Daylightning", and super-low.
Steadyflash is a combination of medium intensity steady light with a flash effect that draws attention, and it is the normally recommended mode for night biking on city streets. I don't believe it is blindingly bright and I keep it pointed slightly at the ground anyway, for the purpose of seeing what's on the ground.
The "high" mode might be overly bright -- I haven't tried blinding anyone with it -- but it's largely intended for night biking in quiet areas with no other lights around.
The Daylightning mode flashes at high intensity very briefly, every half-second or so. It's intended to be used for drawing attention only during the day, and not lighting the way. The package warns that it should not be used at night. Indeed, I find it highly distracting at night, as it creates some of that 'strobe effect' if used at night. Is that what you meant?
None of the watch battery powered lights are "too bright": they are only useful for alerting others to your presence, they cannot light the way.