I will offer my two cents on the matter.
Dive Rite LX 20 for your primary. I have two that get double duty use for cave diving and video lights. It provides more than enough illumination for cave work and plenty of burn time for a dive or two on open circuit. It's cordless so that saves the routing frustration that can come sometimes come with diving side mount. And if it won't provide enough burn time for a full days worth of diving you can swap the batteries for fresh ones on the surface.
For backup lights I'd go with a pair of dive rite BX lights or something similar. They're twist on/off, can use regular alkaline or a single 18650 battery.
If you want helmet lights DGX has two versions of push button lights; one in video/flood the other is a spot. Personally, I think push button lights are better on helmets because they're easier to turn on and off. And they get rid of that pesky cord routing issue.
I have the dive rite lx25...it’s corded, but seemingly twice as bright on its lowest setting than my buddies lx20. It also has a 6 hour burn time...which is nice.
Marci and I both have LX 20 hand helds. I wasn't really a fan until I saw hers in the water, both in terms of brightness and run time.
Dive Right advertises 4 hours on high and 6 hours on medium, but we've both gotten 5.5 hours out of them on high (20,000 lux). If we are planning a 6 hour dive however we'll normally click them down to medium (13000 lux) in small passages where the extra light isn't needed. On medium, they are still slightly brighter than our prior 12W /1200 lumen light Monkey corded can lights.
I also dive on a regular basis with someone using a 24W / 2000 lumen LED Light Monkey and the LX20 holds it own just fine in terms of over all light output, and the brightness of the center spot. And, I've noted that his light will die right around 4 1/4 hours, while mine will still finish the dive. There's no doubt some trade off in brightness for run time, but given the form factor, whatever DR is using for a chip in the LX 20 is really efficient. And as mentioned above, if you are doing two dives per day, you can swap batteries between dives.
Cross team light compatibility is important as you need to ensure that the weakest light on the team can still be used effectively to signal all the other divers on the team. Consequently, part of your selection criteria should be driven by who you think you'll be diving with. If you plan to dive with some one who has a 32 watt / 4000 lumen light, you'll either have to get a light that can compete, or your team mate will need to back down on the power.
Larger lights sound great, but with a given technology, more light requires larger battery capacity (and a larger can) to get a comparable run time, so run time starts to come into your decision making process. For example, my 24 W / 2000 lumen sometimes team mate will find he's got a problem once he works up to dives in the 6 hour range, when is canister light dies at 4.5 hours. And he already has issues in tight passage with the current can size.
In some respects, I suspect we will shortly be seeing the end of the canister light for non video light purposes. The same improvements in LED lights, improved LED efficiency, and improved battery technology that have allowed more light and longer burn times in smaller corded canister lights will I think eventually do away with the canister light in favor of a handheld.
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We back up our LX20s with our old 12W LED Light Monkey heads screwed on to 2.6aH Light Monkey hand held battery pack. That gives us "back up" primary lights with just over 2 hours of burn time in a 2" x7.5" light that easily fits in a pocket, in addition to our smaller helmet mounted back up lights.
This is where I get a little conflicted. Dive Rite has a bad habit of introducing something new every couple of years and then no longer supports their discontinued lights. Yes, I get that improvement is nice, but above a certain level it doesn't make much sense, and it just forces you into a new light.
In contrast, Light Monkey's service is superb and they will support what they make for pretty much as long as you continue using it. Consider our 12 W LED corded can lights. They are several years old, but LM can replace the batteries if needed, and they are still very compact and useable 5 hour 1200 lumen primary canister lights. Or, you can repurpose them as a hand held 'back up' primary, or as a 2 hour hand held primary light for just $100 with a hand held battery pack for them.
Underwater Light Dude is another company that makes superb lights, and will support the product for years after it is sold. Bobby's quality is superb, and he uses a slightly different approach to the corona on his lights which creates a larger usable center spot and less light spillage than some other designs.
All of the above are companies owned, managed and staffed by people who cave dive, so you don't have the corner cutting issues that can occur with some of the Asian companies where low price point is their primary concern.
So the business model of the company is also an important consideration when buying a light. Are you comfortable changing lights every few years, or do you want one light to use for the next decade or so? DO you want to buy lights from people who actually use them, or take your chances with a light designed and produced by people who may never go near the water?