I would use the same choices with brazing and welding.
Brazing is just soldering at temps above what? 600F or 800F? The solder/braze will flow into the lap of the joint and out the other side and that will make a pretty strong joint actually. The fillet on the edge to edge joint with a soft braze or solder will not be as strong as the lap.
The edge to edge joint when welded is much faster to do and will almost be hard not to get full penetration.