UW still photos and video are two VERY different things. Think about the power of video lights vs a strobe. The strobe is MUCH brighter. That's because it only has to flash for a fraction of a second. Correlate the brightness of the strobe/light to the sun and you'll understand why few people use video lights during the day - especially in shallow water. A filter works very well on video down to about 40'-60' during the day. Beyond 60' during the day a video light set becomes useful - but has a very limited range! If you use video lights AND a filter, the background looks normal, but the foreground is too red. If you use the lights without the filter, the background is extremely blue/green. Same goes for using a filter or manual white balance with a strobe on a still camera. However because of it's added power, a strobe will be much more effective at pretty much any depth. The secret for most shots with still cameras is to expose the foreground (stuff in range of the strobe) with the strobe power setting OR f-stop -- and adjust the background exposure with the shutter speed. You can darken the background to reduce the blue/green effect. If you have very bright video lights, you can get this same effect. That's what you see in Nat Geo films. They have million watt lights (well really bright anyway!).
So -- rule of thumb for video. Get the brightest lights you can afford. Take them with you - even on day dives for close subjects at depth. Use a removable filter (remove when using lights) and always use MWB with the filter!
Hope this helps!
Mark