Battery voltage declines from the time the batteries are full until they are empty. When calculating efficiency for a linear regulator (LDO is a type of linear regulator), this must be taken into account somehow. The simplest way is to use the AVERAGE voltage of the batteries over the whole discharge curve. The average voltage of an AA alkaline battery is around 1.3V, although this depends on the load. So with 4 batteries in series, the average voltage will be around 1.3V * 4 = 5.2V. So the average efficiency of the LDO will be 3.3/5.2 which is around 63%.
If you use a buck converter, you can probably count on getting 85% with relative ease. Higher efficiencies are also possible, but you will have to do everything very carefully. So you will get roughly 30% longer battery life with a buck converter.
There is something else to consider. The power dissipation in the LDO will be equal to Iload * (Vin - Vout). Now, here, you have to use the max voltage, not average. So let's use 1.5V. That is Iloud * (6 - 3.3) = Iload * 2.7.
For 100mA that is only 270mW. Fairly manageable. But if your load is 500mA, then that is 1.35W, which will be difficult to manage. So higher currents should steer you away from an LDO and toward a buck converter.
Now let's consider quiescent current. If the regulator is going to operate for extended periods with light or no load, then quiescent current has to be considered. LDO's will have much lower quiescent current than buck converters, although some buck converters are low enough to run for many months (with no load) on AA batteries. Pay attention to quiescent current specification if that applies to you. Also, buck regulator efficiency at very light loads will not be much better than an LDO.
Now let's consider cost. If you are only building one, the price difference doesn't really matter. But if you are mass producing this, keep in mind that LDO's are WAY cheaper than buck converters (in volume). Although this may not be true if you 200mA or more of output current, because then you will need a big LDO or an LDO plus heatsink.
So those are all the tradeoffs. My guess is that you will be better off with a buck converter in your application unless the output current is under 50mA or so, in which case I would use an LDO.