My technical expertise has sadly diminished the last couple of years. But I can give some information that will help you compare flashlights and batteries. My comments are for flashlights using Li-ION batteries and are high intensity devises.

Flashlights

When looking for a flashlight the user needs to consider the primary use. Many Li-ION flashlight are compact using one Li-ION battery. There are some that use two or more but their outputs are much higher than you might need for home use or carry.

The user needs to determined the applied use of the light. I find a flashlight is either a Tactical Light or a General Purpose light. The Tactical light needs a special beam so that in close quarters like a home, the light doesn't blind the user as well as the intruder. The Olight Warrior X Pro is a Tactical light with a 2100 lumens center light.  The beam width is small at the center and there is a lower level outer light. The lower level outer light is wide and fills a room helping your peripheral vision with out blinding you. In contrast my Olight Seeker 2 has a single density light at 3000 lumens and it could be blinding to the user in a smaller room.

The switch can be important. Most Tactical lights have a tail switch. The Olight switch on the Warrior X Pro is a new designed tail switch and is raised slightly to accommodate use with gloves. My older Warrior X has a flat tail switch and not as easy to use as the new design.  The switch on my Seeker 2 is barrel mounted and I like it a lot for use outside where you might want different levels for different applications. The single density light is large and lights a large area. The barrel mounted switch also tells me the level of the light and how much charge the the battery has. I use that feature quite a bit.

There are a bunch of off brand flashlights available. My preferred brands are Olight and FENIX. The off brand flashlights may have cheap plastic bodies and off brand batteries. I don't have any Streamlight or Surefire but they have a good reputation.  

When selecting a Li-ION flashlight make sure you get one that uses CREE LEDs. These are the best available at this time. If you buy a flashlight from Amazon you have to be careful about the batteries if you buy extras. Amazon has a Hugh selection of Li-ION batteries and they are not all created equal. There has been complaints in the reviews of some Li-ION batteries being too big around to fit into their flashlight. Stick to name brand flashlights like Olight and FENIX. Buy the batteries directly from them or if you buy from Amazon, make sure you get Olight or FENIX batteries.

Now if you buy off brand flashlights and batteries, please let me know how they work out.  Li-ION batteries are expensive but have long life if maintained.

Batteries

Before we talk about Li-ION batteries lets discuss the standard batters we use in our Autos and Boats.  They all have an AH (Amp Hour) ratting so a user can gauge the performance for their particular application. 

In my boat I use a 100AH (Amp Hour) battery to operate my trolling motor.  The 100AH battery will give me 100 amps for 1 hour to do work with.  The trolling motor is variable speed and different speeds draw different loads on the battery.  So if I operate my trolling motor at a speed that draws 10 amps, I can operate for 10 hours and then my battery would be exhausted and need to be charged.  If I operate my trolling motor at a speed that my motor draws 20 amps, then it would operate for 5 hours.  Of course the trolling motor isn't running all the time but this gives me a feel of how long I can fish and not deplete the trolling motor battery. 

Li-ION batteries are rated in mAh (milli-Amp-hour).  mAh stands for Milliamps Hour. Milliamps Hour is 1/1000th of a Amp Hour, so a 1000mAh = 1.0Ah. Milliamps Hour (mAh) is important because it's the easiest way to distinguish the strength or capacity of a battery. The higher the mAh, the longer the battery will last.  

To convert milliamps to amps we have to divide the milliamps by 1000.  So the 5000mah Li-ION battery in my Seeker 2 flashlight has 5Ah of energy to run the flashlight.  A 3000mAh battery will have 3Ah.  You can see that a 5000mah battery has considerable more energy than a 3000mAh battery.  This is why I stopped using the 123 batteries with 750 to 900 mAh ratings.  

Since the end user doesn't know the load that a flashlight puts on the battery at different intensities, we have to rely on specifications from the manufacture.  Olight provides run times for each level of intensities that a particular flashlight has.  So level one on a particular flashlight may be 3000 lumens for only three minutes and then drops to a lower level to conserve the battery.  Level 5 may be 5 lumens and run at this level for 12 days. 

So how long our flashlight might run is based on the mAh rating of the battery and the load we place on the battery.    

Frank