Hi all,
To obtain 3.3V, what is more efficient, to down from 4 AA batteries or to boost from 2 AA?

 

Let us assume that you use a buck-boost converter to do either voltage conversion.
If each converter is 100% efficient then they are both the same in terms of energy efficiency.

 

I would use a LDO 3V regulator on 4.5V batteries (3 AAA)..


https://uk.farnell.com/stmicroelectronics/lf33cdt-tr/ic-ldo-regulator-0-5a-16v-dpak/dp/2473998

 

I have used the NCP1402 in a boost configuration. It is really quite easy to do.

Sparkfun, Adafruit and others sell breakout boards for such items. The nice thing about such hobbyist oriented sites is that design information is often given. In my case, I used the SF design, which is basically just the datasheet, and modified it for my needs.

Buck/Boost:
https://www.sparkfun.com/products/15208
Boost (NCP1402):
https://www.sparkfun.com/products/10967

 

Depends upon the relative efficiency of the conversion.
Compare the efficiencies of a buck-converter and a boost-converter to see which is best.