From what I remember, American Arms bout their guns from Uberti.
Beretta owns Uberti. Uberti makes 2 near perfect replicas of the 1873, one with the early cylinder release and one wit hthe later style release.
Uberti makes a third version which beretta markets as the stampede. The only differences between the Uberti and the Beretta are that the Beretta uses a modern transfer bar safety and has bakelite grips similar to 1st gen colts, while the Ubertis are offered with wood or faux-ivory grips and have no transfer bar safety. Frankly, I think the safety adds another possible failure point to a design already known as delicate, so I'd save myself the extra $100-150 and get the Uberti over the Stampede if I wanted one of these guns.
The Pietta guns, on the other hand, are relatively new. Uberti has made their 1873 for many years now and the machinery they are using is starting to be a little old-tech and more labor intensive than the newer gear. This adds to their finishing costs and the end price. The Pietta machinery is much newer and more automated which, they claim, allows less hand fitting during assembly and lower consumer costs. Also they offer less variants.
All the reviews I've seen claim that the Pietta 1873 is every bit the equal of the Uberti 1873. Neither is as good as a real 2nd gen or earlier Colt, but then nothing is these days - not even 3rd gen or later Colts! The earlier Colt remakes were hand fitted and assembled individually in the USA from Uberti rough forgings and that individual attention to each gun really jacked the price and performance up. The work that went into the Gen 1's would be impossible at todays labor casts as no-one could afford to buy them!
Frankly, my next SAA will be a Pietta in .45LC. Marstar is undercutting the Uberti dealers by over $100 per gun and having now seen both in person, I would not be able to justify the Uberti;s additional cost.
That being said, the Black Powder Ubertis are better finished and fit than the Pietta ones. If appearance is important, get an Uberti BP revolver over the Pietta. The Pietta 1860 Army I have works just fine though, but the polishing and grip fit is not up to Uberti standards.