The use of lapped brace vs a morticed brace depends on tooling. A lapped brace can be cut with just an axe and saw, while the mortice will require more time/effort and tools.
How are you holding the lapped braces to the frame? pegs, nails, screws and boarding?
Lapped braces may have a tendency to twist, and come out of plane, if the wood is not near perfect, species choice could have impact, too, like spruce will twist more than pine.
Braces are typically designed to function under compression not tension. Dove tailed half lapped may help in tension. In compression the lapped section is using the fastening, peg, to resist tension along with the shoulder. A morticed brace has more surface to resist the compression.
