Great! What a juicy topic to wax on about.
Functionally speaking (as you asked), there are differences between boxlocks and sidelocks as mentioned above. Diggory discusses this at length and the various highly regarded opinions on the debate in his first book, “Vintage Guns for the Modern Shot”.
From an engineering viewpoint, it would be hard to argue against the boxlock being the better design. There are fewer parts and fewer parts are better as there is less to go wrong. The beauty of the boxlock design lies in it’s brilliant simplicity. Boxlocks are often derided because there are far more cheaply made boxolcks than there are cheaply made sidelocks in circluation. This is actually a tesimony to the design as cheaply made sidelocks do not work for very long, if at all.
Sidelocks are almost always made as best guns these days which further strengthens the notion that sidelocks are “superior” to boxlocks but this is no indication that the mechanical design is better.
The reality is that most people wanting a new, bespoke SxS want a sidelock and interestingly, a new, bespoke boxlock is not much cheaper to make!
Wax on!