I have thought about this a lot. A finger joint exposes twice as much end grain. Fingers expose the full width of end grain for half the end grain of each piece making the join, the equivalent of one entire end grain. A rabbet joint exposes only half of one end grain of one piece and none of the end grain on the other. Thus, for weathering, rabbet joints expose less of the timber that may be more vulnerable to rot.
However, if the joint degrades over time, fingers should be much stronger. But, the weight is almost all carried by the two end pieces and not the join.
I also noticed the boxes often start to rot on the edges where the hive tool is used, not the joints. Then again, wax dipping protects against this.
My thoughts: more a matter of personal preference (or price and availability) as the box will probably fail in other ways before the joints.