If you go to Gunsinternational and look at, for instance, AYA, you'll see plenty of both. Sidelocks have a large removable plate on each side, behind the main action body, on which the hammers, mainsprings and sears are mounted. These parts are contained within the action body hidden by the stock (or immediately behind but attached to the upper or lower tangs) in a boxlock. Both designs work well, but sidelocks are generally more expensive, although much easier to clean the aforementioned parts, since it is not necessary to remove the entire buttstock to get access to them. I hope this makes sense.
Boxlock - A type of action (receiver) for a break-open gun where the lockwork is contained within a box-shaped housing. (see also: Sidelock). A boxlock is superior to a sidelock because although more metal needs to be removed from the action body, less wood needs be removed from the head of the stock---and wood is generally more vulnerable than metal. The Anson & Deeley boxlock, patented in 1875, the simplest, most reliable and most successful action design, is identified by two pins spanning the width of the action, one at the bottom rear and one slightly forward and higher, upon which the sears and hammers, respectively, rotate. Photo
Sidelock - A type of action on a break-open gun where the lockwork (hammer, sear, mainspring etc) is mounted to the back side (inside) of a plate (or pair of plates for a double gun). A sidelock is superior to a boxlock because: 1. Less steel needs be removed from the bar of the action; the action is therefore stronger. 2. The lock plates provide a larger canvas for the engraver's art. 3. Sidelocks have generally been considered a more aesthetically pleasing form. 4. They are often made with secondary, or intercepting, safety sears. 5. Trigger pulls theoretically may be adjusted more precisely. 6. Because of all the above, most makers building a range of guns have usually reserved the sidelock action for their better grades of guns; this last being the most relevant reason why sidelocks are generally considered superior to boxlocks. Photo
This info is courtesy of Hallowell & Co.
www.hallowellco.comJoe