Both of these should be extremely desirable guns if in good condition - not like the leading gunmakers' best grade, but good, and thoroughly functional if in good condition. A high proportion of them were made for the trade, and bear other "gunmakers'" names, including some who never made a gun. So you are both lucky to have guns with the Webley name. They would make whatever characteristics a substantial trade buyer wanted, so great variation is possible.
It is notoriously hard to date British shotguns by style of manufacture, as details, and particular hammer action, were often carried on long after more modern alternatives were available. In general I'd say a foreend with a transverse key is more likely to be 1870s or 1880, and a lever or push-rod foreend release is probably 1880s onward. A toplever action is generally later than a rotary underlever. The former lever type has the advantage of snapping to, while the rotary lever has to be rotated after closing. The rotary lever feels like it ought to be very strong, but breech pressure forces the barrels forward, not up.
Webley, however, were a very progressive maker, and certainly made top-lever shotguns in the 1870s. I have a pamphlet published in 1953 by Eric Bewley, their general manager, and Thurlow Craig, my favourite writer on shooting, fishing, animal psychology and South American revolutions. They print a line drawing of a nicely engraved and surprisingly modern hammer gun, with top lever, double bite locking bolt and doll's head top rib extension. They give its date as 1870, which might be too early, but not by much. Rebounding self half-cocking locks aren't likely to date from earlier than the mid-1870s.
Some people will tell you never to shoot a damascus barrel. I don't think this is necessary, the view I find most convincing being that a quality damascus barrel is safe for the loads it was designed around and proved for, if its condition hasn't deteriorated.
But... It would be unusual to find an old damascus barrel in pristine external condition, and they would normally be browned rather than blued. (Birchwood Casey Plum Brown does this very well.) Similarly, it is unusual to find a really good bore. This one might have had metal removed by outside polishing and inside fine boring, to remove pitting. You really need to be able to measure the bore, and it would be a good idea to compare the wall thickness with similar guns before firing. Remember, the muzzle thickness is NOT the wall thickness, for shotguns always have a concave barrel contour, to avoid excess weight, and the muzzle is thicker, to protect it from denting, than the metal further back.
Another point is that I would want to be convinced the barrel hadn't had dents raised, which if severe, does tend to crack damascus. I don't necessarily mean that muzzle swelling, though I would want to examine it very carefully. This could most likely be depressed by a gunsmith. It is denting near your barrel hand that is really dangerous. You might want to consider amputating the end of the barrels to get rid of the dent, if they are very long. But a gun of this type shortened much below thirty inches, is likely to feel wrong.
Some were proved for smokeless powder, but otherwise, the original load means black powder, or a substitute such as Pyrodex. They can shoot very well with this at close ranges (since they are unlikely to have much choke), but in most of them a modern cartridge is quite seriously dangerous.
A 10ga chamber is very unlikely to be 3in. The standard, nowadays usually replaced by 3½in, was 2⅞in. That is the length of paper (or plastic) which there is room to have entirely straight and cylindrical in the chamber. You can cut modern plastic cases to reload it.