I guess it would depend on the size of the emergency kit, and what else went into the kit, and of course, budget.
Small kits get either single AA or AAA lights depending on what the Radio takes, since its best to keep everything the same format so you only have to stock the kit with one size. Although there is something to be said for being able to scrounge batteries from more places. I also prefer lights with a reversible clip for hat or collar mounting, so you can go hands free. All batteries stored in the lights NEED to be lithiums. Alkalines can be stored separately, but should never be stored in a light for long periods, as they will most likely leak eventually. I tend to keep at least one AAA light around, since you can steal the batteries from remotes, which most people have several laying around.
Single AA lights that I would trust, bright enough for when you need some serious light, yet have a low mode that will run a long time.
*Quark MiNi. bright, small, great modes and runtimes. Flashy modes available if you can remember how to get to them. Does not have a clip, so you would have to rig one up (I use the clip from a fenix LOD).
*Quark standard AA. A bit bigger than the mini, more modes, clicky switch. More throw. Easy to get to turbo.
*Fenix L1T. 2 modes, so simple operation. Clicky switch.
*ITP A2 EOS lower price than the rest, but still a good light. 3 modes, good run times. great light for the $$.
*Fenix LD10 very nice multimode light. easy to get to turbo.
*Fenix MC10 Anglelight. Multimode, with unique tilting head. great for hands free.
Single AAA lights:
*ITP A3 EOS/Maratac AAA great lights for the $$ 3 modes, good power efficiency. Reversible clip for hat mounting.
*Fenix E01 1 mode, great run times, very inexpensive and yet built like a tank.
*Preon hidden flashy modes, great battery efficiency. Downside is the clip is not reversable, so no hat mounting without stealing a clip from elsewhere.
2 x AA lights
*Fenix TK20. 2 modes, awesome durability, good run times. This would be one of my choices for an "end of the world" light. Neutral tint is nice for outdoor work. Probably my first choice for a giveaway emergency kit due to easy operation and durability.
*Fenix LD20 Many modes, but easy access to turbo. Lighter that the TK20, but still decently sturdy
*Fenix L2T 2 simple modes, good reliability, good efficiency.
*Eagletac P10A2 similar to the fenix L2T in operation, but a little less money, and well made. I have the neutral tint version, and I love it.
*Quark standard 2AA Lower low than the Fenix lights, very well made. Great run times.
For headlamps, there are plenty inexpensive ones available, and I dont know them very well. I have a Zebralight H501w (AA, neutral tint) and I like it alot, great for area lighting, and very small. But since I nearly always have a hat, I usually use my Quark MiNi AA, or ITP A3 EOS for a headlamp.
Overall, for a small giveaway kit, I would probably go with a ITP A3 EOS. $21 or so shipped, batteries can be scrounged from remotes. Reversible clip for hands free use. The only downsides I see are that small size is more easily lost (get the gold or red color, easier to find), and probably not the same size batteries as the portable radio.
Personally, if I could afford it, the kits I would give away would have a Quark MiNi AA(modified with a clip), a Fenix TK20, a radio that takes AA.
And an ITP A3 eos, to take advantage of battery scrounging. I would keep an 8pack of energizer lithium AAs in the kit, and load all the lights with Lithiums too. Going with a Quark 2 AA over the fenix would have the advantage of flashy modes, so that would be a good choice too.
In my house, there is no need for a kit, since I have lights everywhere and enough batts to light every room in the house for a couple months probably. In my car I have my Bug Out Bag (BOB in preparedness language), and it has a Fenix L2Dce(older version of the fenix LD20) and Zebralight H501w.
I am in the process of putting together some small kits for family. Since I am on a tight budget, I will probably use the ITP A3 eos lights, if I can find a small radio that takes AAA batteries.