Hi Dive and Climb:
Not an easy answer. In truth, it all depends. Good lighting at depth is a combination of available sunlight, camera settings and camera lux rating. I use a Sony VX2000 and PD-170, that later which has a 1 lux rating. It can give VERY good results with enough surface light provided one understands the relationship between shutter speeds, f stop settings, manual white balance and how close you are to - or how much you want to see of - your subject.
For example, I can shoot fairly good wide angle video at 100 ft of depth in less than 20 FT of horizontal visibility with a shutter speed of 1/60, an f stop setting of 4.0 or 4.8 and manual white balance shifted slightly blue. I like a "darker" video look (I shoot shipwrecks) with natural color. I also use a VERY light red filter for most daytime shooting at depth. The camera "adds" the red and, to a certain extent, an amount of color "gain" that can be annoying. I switched from the VX2000 to the PD170 just because of this issue. Some will say that there is no difference but I can show you videos with identical camera settings and conditions that look completely different.
When you add video light to this mix during the day, it generally WON'T touch most of your video, especially in wide angle because of the light that's ALREADY there (i.e. the SUN!). For me, the big advantage is the gradual illumination of subjects coming toward you. For example, a lot of my diving occurs between noon and 3 PM. So, the sun's straight up meaning every time I shoot upward I'm shooting INTO the natural light, making the subject darker facing me. Video light during the day, with the right camera settings, can gently illuminate the subject and chase away the natural shadow. This can be spectacular with sharks, or other large fish approaching you. The "trick" however, is to illuminate the subject in such a way that the viewer doesn't notice you've added light. That comes with a WHOLE bunch of practice, something I'm still working on, LOL.
Although LED light is rapidly evolving, it still can't match the intensity of HID. HID with tricked out defusion can produce outstanding results. For example, a "common" LED system (say the Light and Motion "SunRay 2000") produces about 2,000 lumens of light with a "color temperature" of 5,500 K. Compare this to a Dive Rite 35/50 HID video light (now out of production) that produced 3,600 lumens of light at even higher color temperature (i.e, it's DAMN white light, LOL!). Even with adding a defuser to "balance" and "soften" the lighting output, you still have WAY more illumination.
BUT, IMHO, LEDs will ultimately have the advantage because the technology continues to evolve and become cheaper. I wouldn't be surprised if LED replaces everything (including home lighting) in the next decade. On top of that, "flat panel" LEDs are right around the corner and if they can adapt THAT for underwater use, WOW!
So, long of it short, if you want to shoot home movies underwater and not spend a ton of money, get the housing, consider a 10 to 25 W video HID light (they come on e-Bay regularly) and try it out. Do remember that shooting underwater video ain't cheap so know going in that it CAN and most likely WILL get MORE expensive than you thought...
Good Luck!
Andy
! The Nocturnal Lights are worth looking at, for the output and price, they were nice. You will see the LED's are starting to get priced a little better, then a couple months ago. The one thing you have to watch about the HID light is the cost of bulb replacement. And you will be fine, just don't drop them 3 - 4'. They get like 1000 hours or something, which is a lot of time. And with most HID they have a 3 second recycle time. But as mentioned, the HID are very bright, and strong.
