I have that splice book. It includes NOTHING on the locking Brummel. I learned about that here at AS.
With your splice, you weave the tail back and forth through the rope, and it can come back out the same way. The locking Brummel sticks the tail through the rope, but then sticks the rope through the tail, then the tail is buried inside the rope. Loose in your hands, you cannot pull out the tail unless you break the rope.
While this makes a big difference in the security of the splice pulling out when not loaded, it doesn't make it any stronger. Lock stitching does the same thing. As many threads here have shown, particularly Moray's testing, the conventional splice just doesn't come apart under a load, it breaks where the taper joins the rest of the rope.