To me, it makes a bit of a difference WHICH trapdoor you're looking at.
I believe there is a difference between an original and a more modern reproduction. Not in the total overall usable strength, but in what ammo should be used.
Smokeless factory ammo, the 405gr @ 1300fps (approx.) is made to be "safe" in all Trapdoors, meaning it does not exceed blackpowder pressures (and speeds).
There are some folks who believe that while "safe" modern smokeless ammo is not "good" for the original rifles. They will only shoot black powder and lead bullets.
It is known that jacketed bullets are hard on the barrels of 1870 era firearms. The old barrel steel is not the same as what is used today and jacketed bullets (though at the correct pressure and speed) cause more wear than lead.
There is also a belief that even though "safe" smokeless loads are within their pressure boundaries, the old rifles are subject to different stresses shooting smokeless than they are shooting black powder, and that difference increases the failure rate or the old guns.
There is no proof, (currently) but some folks believe that, and only shoot black powder in their originals. If I had a gun pushing 150yrs old, I'd stick to black powder, too.
When shooting any Trapdoor, avoid all ammo listed as +p, or for the 1886 Winchester, and do not EVER allow a round loaded for a Ruger single shot, or a converted bolt action to be put in a Trapdoor. They are seriously overpressure for the Trapdoor action. Dangerously so.
If you've got a modern reproduction like an H&R or one of the quality Italian made guns, Remchester standard 405gr jacketed ammo is fine. If you've got a gun made before 1900, the same ammo is safe, but I would consider only using black powder and lead bullets in a gun that old.
Avoid every load made for "lever guns" and absolutely avoid anything made for "modern single shots or bolt actions".