Here's how I see it. Both 1xAA and 3xAAA have their advantages. The advantages of 1xAA are as follows:
- Doesn't require batteries in multiples of three (which is always awkward, since batteries are typically sold in twos and fours)
- No potentially unreliable battery holders to worry about
- MUCH easier to change the battery on the run
- 1xAA lights are generally more compact
- Extra batteries are easier to carry
- Although a 3xAAA light need not be low quality, quality 1xAA lights are easier to find
Advantages of 3xAAA
- Simpler, cheaper, and more efficient drivers can be used
- Due to higher voltage, lower driver losses, and fewer cost constraints resulting from high driver current requirements, higher power is possible
- Lower current requirement from batteries, even in comparison with internal resistance (which is about .05 ohms for a NiMH AA and about .08 ohm for a NiMH AAA).
So there you have it. Interestingly, all of the advantages I see with 1xAA are convenience related, while the advantages of 3xAAA are performance related. Keep in mind, though, that not all lights of a particular battery configuration necessarily take advantage of these. This is particularly true with 3xAAA lights (which often tend to be cheap, low performing lights).