... as I said, there are tons of different solutions to this. Space, weight ... all can influence what solution is prefered. On my shoulderpieces, I use 3xAAA's too by the way but not because of a deliberate choice but because I had the batteryholders around anyhow.
But just for arguments' sake :
I like the 9V as for 2 leds at 20mah setup, they'll run more than long enough for any convention. As I use rechargable batteries everywhere anyway "cost" is not a vector in my case. I'm not a big fan of the format myself, but I won't be blind to the fact it has its uses and place in the industry.
The 9V block has the advantage of being simple and easy and you don't even need a battery holder : a simple 9V clip, battery is taped or velcro'd in place and you're ready. No risk of battery connection corrosion due to the way the battery is constructed so little to no chance of bad connection over longer periods of time. Simple, one piece replacement when needed. In terms of weight and size, NO other solution can produce 9V on such a small footprint and at such a low weight.
Off the head calculation on the burning time : weak rechargable 9V battery roughly is 250mAh. 20mA full lid led. 250/20mAh : that gives me 12 hours of running time.
Alkalines will run longer. Not sure how much longer as I haven't used Alkalines for years now.
And lets be honest : when you suit up, you'll be making sure you'll be using fresh batteries anyhow, as you've NO idea if those batteries from last weeks convention will really get you through the next one. So if price is something to be worried about : get yourself rechargables no matter what format of battery you're looking at and charge them the night before. Ready.
I can run leds from a LiPo too if I'd really want, they would even run much longer than a set of AAA's and if anybody's into Airsoft chances are they've got those around anyhow.
Just saying, there's no "best" solution for everybody : all depends on parameters only known to the person who's asking.
People who don't want to mess with soldering can use Fingerleds : cost next to nothing, no soldering needed but I'm not a big fan of them as they tend to be a bit iffy in terms of reliability.
They run on 3xAR13's or comparable, and they'll run for 6 to 7 hours with ease. In terms of price, this would undoubtable present the cheapest solution.
The Polytube solution
peterthethinker presented is very nice.
I used a more simple solution : a piece of frosted plastic as window and a metal-film reflector in the inside of the armor to diffuse the lightsource yet amplify the light performance itself. Reflector was made by simply bending a flexible piece of plastic over the light port and coating the inside of it with silver metalic repair tape.
Voila, costs next to nothing, nice bright light without clear "light source" origin point.
PS : not sure what kind of 9V batteries you have over there, but any fresh 9V will give you 9V and nothing else. And if you use them for what they were designed to do in the first place (low power electronics), they will do so in a stable manner and over a more than ample enough timeperiod. The complete electronics of my MA5C/CB88 runs from a single 9V block, including ammo counter and display, at least 4 much too bright side leds .... and I've NEVER run out of juice unexpectedly with that one.
All 9V blocks consist of regular 6x 1.5V cells setup, that gives you 9V which I'm sure you are fully aware of.
There's no escaping this pretty straight forward basic principle that produces the 9V in a 9V block.
Not 7.5V or whatever.
Rechargables will give you 8.4V when full as the NiMh's as a fully charged single cell will be rated at roughly 1.4V when no load is applied.
Using a central fed system like Peter proposes is technically speaking very nice and as a Tech, I Like it.
It's an elegant system.
But it opens a new can of worms.
Reliability of the cables boom and trying to hiding it.
Not to mention catastrophic failure if your central feed goes down for whatever reason.
A simply battery system setup : No light ? Change battery. Works
A Central feed system : No light ? Erm ... let me get my mulitmeter/digital scope/batterytestst ... oh no wait, I don't have those at hand when I'm on the floor.
And that little detail techs tend to forget : cost-effectiveness for a thing that will be used maybe 4 times a year making even those cursed 9V look cheap.
The only way to make this worth your while is if you'd develop this as a central non-suit-specific harness system, which you could use and re-use on every new cosplay suit you're doing. And even then, you'll need several suits to make it a break-even.
I'm not saying you're wrong Peter : pure from a technical point of view, I agree with the beauty of such a system.
I'm not even pretending my solution is better as it is NOT : it is crude, primitive and electrically pretty ineffective.
But using it will be the best and most cost effective solution for anybody who does not care for the technical beauty of a central fed system, and who's just looking for a reliable, cheap and working system which the user can "debug" in the field with a near absolute certainty of getting it to run in case of problems while having next to no knowledge of electronics.
Hence no, I wouldn't dare to say "ditch 9V batteries" as they have their place in electronics and work perfect when used for what they were designed to do.
Neither would I dare to say "central fed systems for everybody" as unless you're into this fulltime and have a lot of suits or/and have a soft spot for designing technically elegant solutions which you yourself can maintain and repair in the field when needed, it will not be the best solution for most of us.
I'd rather say "ditch non-rechargables no matter what type" as there's little to no excuses left to use alkalines these days unless you're dealing with electronics that do need the full 1.5V rating of a single cell, and using rechargables will always turn out to be the cheaper option in the long run, certainly if you do NOT use them ONLY sitting idle in something like a cosplay suit for 99.99% of their operational life time but put them to good use elsewhere in a household instead when they're not needed to power up a Spartan fending of some alien invasion.