No double is "strong" if you are compairing it to a good bolt gun. In reality the double rifle is one of the weakest actions but we have to take that in perspective.
A double rifle uses low pressure cartridges and can deliver two shots faster then any bolt gun. It also has the advantage of having the ability to fire even if we have a dud in one chamber with no more effort then moving your finger to the next trigger. Strength is thus relative, as it depends on your deffinition. However a box lock, stock wise will be stronger then a side lock as the reciol is against two rather large slabs of wood compaired to the side locks four slim fingers of wood. If you are looking for a good used double then do some home work as there are a lot of great guns out there which do not have names that inflate price. (Like Army Navy) and can be a good buy.