Forgive an ignorant old fart but I find that it depends on a combination of factors. As someone who has done a lot of driving in fog, working in fog at roadside, and just plain walking around in a fog
crackup:
) please permit the following observations and questions and whilesome of this applies to headlights it works as well for flashlights in most cases.
Is it a matter of seeing or being seen? I have been in situations where seeing was less important than being seen. Oncoming drivers notice bright glow in the fog better than pencil beams. Seeing a reflector can be easier with one type of light or beam pattern and can be more important than actually seeing down the road or path.
Seeing in the fog with a light depends on several different factors in my experience. If you are driving with pencil beam fog lights that are properly aimed and positioned (mounted low on the vehicle and aimed at a downward angle) that works better for me than an equal amount of light that is either mounted higher on the vehicle or aimed "flat." I know of several people who would even drive with their headlights off and run only with fog lights. Most people who have ridden with them agreed to some degree. However I know of others who insist on high beams and for those people it seems that the ability to not be blinded by the spill and extra lumens is more a matter of their physiology than the lights since people riding with them mentioned it being close to being snow blind. The same things can be said to a large degree about walking in fog (some likea narrow, low angle beam and some like a really bright wall of light).
Something else to consider -- color (tint and/or temperature) also deals with a matter of contrast. Some situations benefit from perceived changes in the background contrast. For instance, conditions of snow and or fog where seeing the terrain of the road is as or more important than distance comes to mind. If the road is rutted or the ditch blends in with the road (especially nasty in a combo of fog and snow), distance can be a secondary concern and contrast becomes a significant factor. Ditto for walking in fog and snow.
Like most things in life there are more than a few considerations and more than a few viewpoints (literally). People tend to think of light as being used only for aiding general vision and not about it being important so they are able to be seen as well. Additionally being able to see reflectors and discern shapes can sometimes be more important than seeing in detail.
It's important to consider more factors and to think about things "in three dimensions."