From a purely practical standpoint, the wood and action on the boxlock is stronger and more reliable in the long run, but that is not to say that the sidelocks are flimsy or should be avoided. Either design, well made, will balance, point, and swing with equal grace. There is little doubt that, with the possible exception of the Scottish round-action trigger plate guns, the sidelock is the racier looking item and represents the high-end art of gunmaking.
In a side lock, the lock (hammer, sear, hammer spring) are part of a side plate that is not part of the receiver. In a box lock, the lock is inside of a steel box (receiver).
I have many times made fake side plates for a box lock gun to create more area for engraving.
I went to England many years ago to have a H&H made for me. I was firmly told by the master gun fitter that the "aristocracy and gentry would only shoot a side lock gun". I did not tell him that I was a backwoods boy from the Blue Ridge Mountains. I followed him and received the very worst gun fitting I have ever experienced. I learned from this "Master" that the cheek should never firmly touch the comb. Unfortunately, from time to time, when I am on the line, I follow his advice.