I have been researching batteries some while shopping for lights. I also have some experience with different single use battery types and basic rechargeable types. Here is what I have learned so far.
The high quality alk. single use batteries have 10 year shelf life. Lithium can have 15 year shelf life.
Rechargeable NiMH have the most bang for the buck if you use them a lot and charge them a lot. They have low shelf life. They loose like 1% power per day. Best used for your camera and stuff that drains them fast. We use a lot of them.
Rechargeable Li-ion batteries like the 18650 and others have more output power and longer run times. Depending on the driver in a light, they may put out more lumen or them may just have a lot higher run times. On the down side, they have a life of only 3-5 years if you use them or not. Stored in a cool place not fully charged will extend the life. Laptop batteries usually only last about two years because they are kept fully charged a lot and warm a lot. On the upside, they have a much better shelf life for drain down than NiHM. So they are great if you don't use them for a while and then really use them a lot. They really are not as practical if you don't use them a lot because you will only get so much time out of them before they go bad anyway. It is best to run them down a ways and recharge. Total drain down does shorten the life. The li-ion is great for heavy users like night workers, pest inspectors, military, rescue and so on. They use them a lot and really need max run time when they have to have them.
In my mind, the high end rechargeable are good if you use the light a lot all year or if you are doing remote hunts where you will use the light a lot and want max run times with minimal extra batteries along. Then you get your moneys worth. If you only use your light during hunting season a short time here and there, and only seldom off season, you may only get a few high demand uses a year so not a lot of use for the powerhouse rechargeable battery in 3-5 years before it is shot. For the same money you spend on the li-ion battery you can get a couple sets of single use lithium batters that will be there when you need them for 10 or 15 years self life and likely cover the same usage time if you don't use it a lot over that 3-5 years. Cold be a break even not counting the charger.
I use a couple LED head lamps hunting getting in, out, setting decoys, setting stands, tracking, and gutting animals in the dark. I use them on and off for power outages, night walks in winter months, building inspections and general use over the year. I get about a hole year out of 3 AAA or 2 AA batteries if I just use one of the lights for everything. I have a couple so that doesn't happen now days. I am on year three with high end Duracell copper tops in the one I keep in my waterfowl bag. Having a high end battery in that light would be a complete waste. I do have to say that I only use as much light as needed for the task. I don't go lumen crazy with my LED lights. I use the lowest setting I can for what I need to do. All but one of my LED's are muti level lumen outputs.
The Li-ion top type is dependent on the device. I kind of like the button top because I am less likely to put them in backwards. You have to check to see what any particular device require. Most laptops and other items that only use the LI-ion battery use flat tops from what I have seen, but that may not be the case always. I know some require button top like my new Eagletac. I would assume that a light that uses CR123's or other single use batteries also would be more likely to need a button top. I think some lights can use either flat or button top if the contact points are set up to work with either and battery length is not an issue. I am fairly certain I read up on one light that took both. I have seen where you can get a magnetic button to put on flat top batteries so you can use them in devices needing a button top.
I am starting off with CR123's in my new light, but my light takes the RCR rechargeables and the 18650. I have all kinds of options and that is nice. I personally don't think I would get a light that only took the rechargables. I figure I should easily get well over a year of typical use out of about $3.50 in batteries if I don't go crazy with the high output modes. I was able to get 10 of the higher end longer run batters for under $20 shipped. There is even better deals than that for the middle of the road batteries with slightly less max run time. I will see how controlled I am. Blasting stuff with 600-800 lumens is kind of fun.