Neiher. In break open actions the trigger plate lock has neatly solved the "problems" Burrard mentions re the boxlock while also avoiding the real problems of the sidelock, which Burrard conveniently forgot to mention. Stock cracking, too many parts, plates that span metal and wood, the list is a long one for the sidelock. I would add the shameless copying of the H&H action by indifferent makers who reduced it to something that barely deserves the title "gun".
The archetypical trigger plate action is the Dickson, which also happens to be one of the best looking guns ever built. "For sheer thoroghbred lines the DRA yields nothing, nothing whatsoever to the finest sidelock ever built" Gogh Thomas, who owned Atkin and Purdey sidelocks wrote this.
Other proprietary actions, like the French Ideal, the Beretta 626, the Model 21, are sufficiently different from an Anson-Deely boxlocs as to evade the old criticisms, and all are more robust than a sidelock.
So let's move on from this old quagmire.