I don't see the locking miter as having anything but endgrain. If you look at the earlier link the piece shown has long grain exposed by the cutter but the mating surfaces are all met with end grain from the other piece. The locking miter improves glue surface area and is probably very strong. Box joints have end grain-to-end grain surfaces which are even stronger.
There have been many post on this forum where posters have indicated a preference for TitebondIII and even go as far as to point out a study where TitebondIII was shown to be stronger than the polyurethane glues. I don't doubt this conclusion, but for making bee boxes I much prefer the poly glues because a judicious application caused enough foaming to fill all the joint with some left to spew beyond. Protecting the joint from water is critical, and the foam makes a protective seal around the joint. Some end grain on the fingers still need to be protected with paint of you want them to stay dry. Any water that gets into the joint will cause expansion and contraction, which will weaken the joint over time.
I use roofing staples to hold the joint together while gluing and have found that the force from these larger staples has a tendency to pull the joint together. If I didn't have the stapler, and didn't want to use a million clamps then I would probably use the TitebondIII because it sets up much faster. Also, the poly glues are a sticky mess that you have to put up with if you like the benefits. Since I am lazy, I like to use box joints with poly glue, roofing staples and a few coats of high gloss exterior alkyd paint. By lazy, I mean I don't plan on building the same box twice. I have also found that I can save a little time and money by mixing a good oil base primer with the high gloss alkyd. The oil base paints are good because they penetrate the wood. If they take all week to cure, though, it can drive one nuts. So by mixing the two paints, you keep the high solids content while adding a little extra hardener. My boxes are usually dry enough the following day (in summer) to handle. They should be stacked in an alternate pattern, however, or you will be prying boxes apart later.