The 123 family has several characteristics, many of which do not make them so good for bike use IMO.

The non rechargeable CR123 has good current delivery for its size, low weight, good cold temperature performance, and long shelf life - unless you get inferior ones, which are generally Chinese imports. However, they can catastrophically ignite and vent with flame and toxic smoke, especially when used in multiples (series) when cells can get unbalanced. Many feel this is much more likely with the poorer quality control product. I stick only to US made CR123s now myself. I never had flames, but I had a lot of import cells lose most of their capacity after a few years on the shelf, instead of the 10+ years for good cells. Nominal voltage is about 3.1 volts. Good cells can be had for about $1.25 each in modest quantities on the internet.

The rechargeable RCR123 cells usually have a protection circuit built in to prevent overcharge or over discharge; this means the room for chemicals is reduced on top of the reduced energy from lithium ion over the non rechargeable. Unprotected cells are available, but you have to be very careful to prevent overcharging or discharging below about 3 volts. Off the charger, RCR123s are about 4.2 volts, enough to blow some lights or make them run in their unregulated zone until the voltage sags. The current draw is also less than nonrechargeables, IIRC.

Single 123 lights have limited runtime for bikes, and IMO double 123's are not much better and have many headaches and dangers. 18650 packs seem to have become pretty standard, but the Magicshine recall probably illustrates that all batteries have dangers, even more so in packs. There's a lot of energy in these things.

I personally use AW RCR123 cells and have been very satisfied for several years, but I use them for pocket lights, knowing I can get at most 1 hour of 100 lumens or so. Lighthound and 4Sevens have them, about $8-9 each.
My NiMH AAs and AAAs are Sanyo Eneloops.