Hi there,
Buck converters are usually regulated so the output remains constant also with a higher efficiency.
They all have an efficiency rating too though, usually around 70 to 90 percent, with the majority coming in around 80 to 85 percent. It also depends on the input output differential though, and also on the load current.
Because the efficiency isnt perfect (like 80 percent typical) that means that sometimes it will be no better than an LDO linear regulator. That is when the input voltage is ALMOST equal to the output voltage.
I suspect this is the case with your setup if you have 6v in and 5v out, especially because that 6v comes from four AA batteries which load down pretty quickly once connected to the circuit. Before you know it you will have 5.5v in and 5v out, which means a common buck circuit that is not designed for super high efficiency will actually take MORE power to run than a linear LDO regulator.
There's almost no doubt here that an LDO would be better or even no regulator at all and just a series diode like someone suggested, but to figure it out for sure you only need to calculate the power wasted by each scenario: the buck vs the LDO.
For the LDO, the input is 6 and the output is 5, so the efficiency is 83.3 percent...not too bad already. When the input loads down to 5.5v, the efficiency is up to 90.9 percent and that will happen pretty quick really. It would take a really good buck design to get close to 91 percent.
It should be clear that a buck with 80 percent will loose to both of these scenarios, so it is not likely that a buck will help at all unless maybe it was designed very carefully.
The series diode is another consideration. If we consider a Schottky then we might assume a 0.5v drop (although that must be tested for). Given that, with 6v in and 5.5v out we get 91.7 percent efficiency, which is quite good really. With a regular silicon diode we get about 0.7v drop, so the efficiency is about 88.3 percent, also not bad, and the extra drop is a little better when the batteries are new because the total voltage could be a little over 6v.
One of the other points is that the battery voltage runs down over time, little by little. This means the board will not get a stable reference with four AA batteries and a non regulated setup. On the other hand, if using an LDO once the input voltage gets too low the LDO may not be able to put out much voltage at all. That's a big problem, because AA batteries run down and there is usually a lot of energy left in them even when they get down to 1.4v each which translates to 5.6v, so the LDO has to be able to work down to at least maybe 5.2 volts.
There may be other possibilities here too though, such as using 3 AA batteries like someone suggested and then using a 3.3v regulator (or something like that) to regulate the reference voltage for the ADC, and use the ADC reference pin (with series resistor for protection). That will give you stable voltage readings while not having to regulate the main power.
Logic circuits dont always need regulated voltage, it's mainly the analog parts of the circuit that needs a stable reference in order to make reasonable measurements. This allows us to do stuff like only regulate the reference voltage for the ADC. There are different types of regulators in a class known as "reference diodes" that are made for this very purpose. They provide a highly stable voltage for making measurements using the ADC.
Good luck with it 
