For serious organised search and rescue there is an argument that you want as much light over as wide an area as you can possibly get as this maximises your field of vision and reduces the area of ground you need to cover on foot.
there is also the consideration that a bright light is more likely to pick up a flash of reflective tape etc on a casualty's gear.
However there is a counter argument that unidirectional artificial light will never realistically give you the same visual acuity as daylight and at night a bright torch can produce tunnel vision where you only concentrate on the illuminated cone and can ignore more subtle clues from your peripheral vision or other senses.
Similarly if you are searching for a casualty who is using a small torch or chemical light to signal then a very bright light may actually impede your ability to spot them.
Clearly there are different situations, for example between a small group searching a hillside for a lost hiker vs a long line of people combing a wood for a lost child.
There is also the consideration that for a serious search at night on open ground an aircraft with thermal imaging equipment will have the large area/long range aspect covered far better than any search on foot so a foot search may be more concerned with short range vision in dense cover (woods, buildings etc) where light output is less important.