It looks like most of the lights sugested are more for scuba than freediving. They are good dive lights. Just not what comes to mind when I think of freediving. I will list a few lights that I would consider for freediving, including what I currently use. They range in price from $15 to $600.
First off, your light selection will be determined by type of diving and preference. The majority of my freediving is into spring, caves, and caverns. Mostly daytime, but some night dives. I like to have my hands free for equalizing and pulling along ledges when needed. This is a primary factor for me. It also lead to creating my current set up.
My primary freediveing light is actualy a secondary light for scuba. I typicaly use a Princeton Tec, Tec-40. It is compact and only uses 4 AA batteries. It is a twist on design, which has a unique side effect which makes it so great. And it only cost $15-$20. Cheap, but very good. This is not the brightest light, but its bright enough. During the day, in caverns, it will light up a 20ft. wall 40ft. away, and everything between. At night, it seam even brighter and will project over 100ft. in clear water.
This is how I use it. I take two rubber snorkle loops, pinch the holes together and slide them over the body of the light. This creates two loops on the light. I then slide a velcro strap threw each loop. This allows me to strap it to my arm. With the twist on design, I twist the cap until the light turns on, then back it off until it just turn off. Now if you push on the cap, the light turn on. And when you release it, it turns off. What makes this nice is that as you descend, the water pressure will automaticaly turn it on at about 20 ft. And on your ascent, it turns off at about 10 ft. This feature turns it on right when I neen it, and saves my batteries. By placeing it right behind my wrist. If I need it to turn on sooner, all it takes is a flick of the wrist, bumping the light.
Underwater Kinetics makes two similar lights. The mini Q40 and the mini Q40 eLed (LED). The mini Q40 acts the same as the Prinston Tec, Tec-40. The mini Q40 eLed has more of a white light than the others and the batteries last longer. It does not turn on as easalt with water pressure as the others. But at night you want to leave it on anyways, so the extended battery life comes in handy. The mini Q40 cost about $17-$23, and the mini Q40 eLed cost about $25-$30.
Your next options are canister lights.
Nite-Rider makes several compact lights that range from $200-$700. You can get them in Halogen (5 watt-32 watt) or HID (10 watt) models. These lights have a very small battery pack that clips to your weight belt and a cord connecting to the light head. The light has a hand mount with optional head mount.
Dive Rite also makes a slim-line HID canister light for about $450-$700. The battery pack for this light is less than 2" in diamiter, and can be mounted to your weight belt.
There is another company that makes really slim line HID canister light that range from 10 watt - 100 watt, but they also cost about $1500 and up.
Remimber, a 10 watt HID is equivlant to 40-50 watts halogen.
The light listed by everyone else are all good lights. These are just to give you some hands free options, which I find to be a very helpfull feature. In the end, it comes down to use, enviroment, and preference. I hope this helps.
Brian