I own and shoot a reproduction 1873 Trapdoor Springfield, which I purchased new in 1977. It was made by Harrington & Richardson and is the Little Bighorn Commemorative carbine.
It is the cavalry carbine with short barrel (I think it's 22 inches but it may be 20. I'm at work and can't check).
Anyway, I've been reloading for it since 1977. When I first purchased it, I asked this very question of Harrington & Richardson.
I was told that whilie the steel is of better quality than the originals, the design itself is the limiting factor. For all practical purposes, it is no stronger than an original in the same condition.
I was warned against using any loads that exceeeded those recommended for the original 1873 Springfield and I've done that for more than 25 years.
So, no, it is no stronger than an original 1873 Springfield in excellent condition. And many Trapdoors are not in the greatest condition, so I would not exceeed the recommended starting load with smokeless powder.
Interestingly, the late gun writer Elmer Keith wrote numerous times that the Trapdoor Springfield should NOT be used with smokeless powder. He believed its action was too weak. I don't agree with him on this and believe that, if the rifle is in good condition and safe, it may be used with low-pressure smokeless loads.
A word of warning: There are some cartridges that attract ignorant maniacs, the .45-70 is one of them. I've found loads on the internet, listed for the Trapdoor Springfield, that are clearly too much for it!
Your best source for good, safe loads remains the reloading manuals. I suggest Lyman No. 48 reloading manual as it has a section on loads for the weak actions, such as the Trapdoor.
Also, Handloader's Digest No. 7, dating from the 1970s, has an excellent two-part article on reloading for the .45-70 with lead and jacketed bullets, in various action strengths. That article was originally published in Handloader magazine, I understand. It remains one of the best articles of its kind, despite being 30 years old.
The reproduction 1873 Springfield is a hoot to shoot. With a little practice, you can get four to six shots a minute off that would make life difficult for any aggressor out to 200 yards or so.
Some people still chastize the Army for adopting it over the Sharps but the Trapdoor --- when used with black powder loads --- had it all over the Sharps as a combat arm. For one thing, it threw the empty case clear of the breech, whereas with the Sharps you had to pull the extracted case out.
I've read quite a bit about the Trapdoor over the past 30 years or so and decided that a good one was marvelously accurate, and marksmanship records bear this out. However, it was often hindered by subquality ammunition and standards of manufacturing.
I recall reading one gun writer state that he has made it a practice for some years now to measure the bore of every 1873 Springfield he could. He's found them with dimensions ranging from .452 to .462 inch. With such a variation, accuracy suffered no doubt.
But the soldier who had a good one, and knew how to shoot, and had good, fresh ammunition, could hit man-sized targets out to 600 yards or so.
One of my old American Rifleman magazines from the 1930s has an interview with such an old soldier, who was on his Army post's shooting team. When it traveled back East to compete, once a year, the soldiers chipped in and bought their own, fresh, commercially made ammunition rather than use the older Army ammo that had been stored for years --- often in questionable circumstances.
He said that Army ammo, by the time it reached Western outposts and forts, had bullet lubricant that was typically dried out. This lack of lubrication cause terrible leading and accuracy was usually so-so to atrocious.
But if fresh ammo was used, with a lubricant soft enough to keep the black powder fouling powder soft --- and if you had a rifle that had a good bore --- it was an accurate rifle. He and his teammates won many matches in their region and back east, solely by using fresh ammunition.
My reproduction Trapdoor is well made, has a nice .458 inch bore and is accurate with black and smokeless powder.
It's a fun gun. It may not be as accurate as the highly refined Sharps reproductions of today on the target ranges of today with their extremely long ranges.
If you want a fun, unusual .45-70 it will surely draw a crowd at the range. Everyone seems fascinated by its action and history.