"Personally" I'd take the side lock. Sidelocks have just always had an appeal to me that is totally lacking in a boxlock. I say this even though my earliest experiences with doubles were all Boxlocks.
Not having deep enough pockets to afford the truly "Beats" my personal favorite has become the American Lefever. Yes, I am fully aware it is technically a Boxlock, but it has far more in common with a normal bar-action sidelock than with a true boxlock. Also, the side plates are not just "Falsies" but expose the lockwork when removed.
I have a Birmingham side lock of lower quality than a Best, a J P Clabrough & it has shown no tendency of being in any way an inferior gun. It is a pre-1900 gun, likely around 125 rs old & since I have had it has had one broken part, a stirrup connecting the mainspring to the hammer. This was at least 35 yrs ago. I made a new one for it & it is still going strong. It is a 6 lp 14 oz 28 barreled Damascus. I habitually shot it with 1 oz loads at around 1125 fps @ about 8K psi.
