Found a nice app note by TI, and wrote some thoughts on it:
Just recently read an app note that targets your same circumstances. Using power solutions to extend battery life in MSP430 applications By TI's Michael Day. While it uses the MSP430 as its target, the same applies to any MCU.
Depending on the MCU's Current vs Voltage, and Voltage vs Clock Speed, using an LDO with a low Quiescent Current will be much better than powering the MCU directly off the battery. The example uses 2x AA, and a TPS780xx regulator with 0.5µA IQ, at 90% efficiency. The active mode current difference is ~175µA!
The lower the clock speed and input voltage, the lower the current used is.
In this second example, System 1, with the MSP430 powered directly from the batteries, operated for **223 hours before shutting down**. System 2, which used a TPS780xx to drop the MSP430 operating voltage to 2.2 V, operated for **298 hours before shutting down**. The addition of the TPS780xx LDO, which operates at 90% efficiency with these operating conditions, extended battery life by 30%.
Later on, it even compares the Low Power Mode/Sleep currents:
In low-power mode 3 (LPM3), the MSP430FG4618’s operating currents at inputs of 3.3 V and 2.2 V are 2.13 μA and 1.3 μA, respectively. With the TPS780xx’s 0.5-μA quiescent current added, the battery currents are 2.63 μA and 1.8 μA, respectively. **DVS reduces battery current by 26% under these conditions**. This reduction of LPM3 battery current is critical for systems that spend a significant amount of time in sleep mode.
While specifics are important, using a low Iq LDO, and targeting the lowest voltage your MCU and the radio can use, you'll cut down on the current required compared to straight off the battery.
Considering the MSP430 launchpad ICs use 1 MHZ as the default calibrated clock, powering it at 2.2V would be significantly better in battery life.