They are the same price. What is the difference?
Butterflying involves cutting most of the way through a piece of meat the long way and then opening it like a book. This aids in cooking the center, and normally doesn’t havr a bone because you can’t cut through with a bone. It does not refer to any particular part of the animal.
America’s cut is a lean, less flavorful loin cut without any bone.
So is the difference just how well they cook in the middle? Does the butterfly cut taste better?
Cooking means there is heat outside the meat making the meat hotter (and breaking down proteins, of course, that make cooked meat different from raw meat even after it has cooled again). When a cut of meat is thick, cooking becomes more of a challenge: high heat will cook the outside of the meat correctly but the inside not so well. And if you continue to cook until the inside is cooked correctly, you can end up with a section nearer the surface that isn’t as palatable.
Barbecue smoking and sous vide cooking both seek to minimize that issue by cooking at lower heat for longer periods of time, so that the outer and inner portions don’t differ dramatically.
But any cook is made easier when the cut of meat is (a) uniform in thickness, and (b) not very thick. So butterflying a cut, or spatchcocking a chicken or turkey (same thing as butterfly: you use shears to cut out the spine and then flatten the bird before cooking to create a more even and quicker cook) is just a technique to make getting an even cook easier.
(Off topic, but sous vide delivers an even cook beautifully, but because the sous vide never rises above the desire internal temperature, the meat’s exterior is never browned, which is not just a cosmetic flaw. The browning, or searing, creates caramelization of the exterior and a process called the Malliard reaction, which produces the desirable flavor. This is why sous vide meat needs to be seared after the cook is finished.)
Butterflying is just a technique to ensure even cooking, and it doesn’t imply a quality level. What the butterflied chop tastes like after cooking depends on what caliber of meat it was to begin with.
Unless of course you don’t want the maillard reaction, I sous vide chicken breasts instead of poaching, i seal fish and seafood with butter and flavorings (takes a fuckload less butter than doing an open vessel butter poach!) and anything else i dont want browned.
Back in ye olden days thinner cuts of pork like butterflied were probably preferred because unlike a good steak, pork was always cooked well done. But these days pork is much safer, and the USDA says an internal temp of 145F is fine. Cooking, say, a pork tenderloin to 145 results in a nice juicy cut of pork with a little pink in the middle, and much tastier than the thin, dried out, well-done chops of yesteryear.
Butterflying can be used to open a thick chop for stuffing. Otherwise the result is the same as slicing the pork more thinly to start with, when unfolded it’s just two thinner chops stuck together at the side. It makes some sense for center cut chops or pork loin which is tender enough to cook quickly.
Our chef at a steak house I worked at (I’m old, almost 5 decades ago) would routinely go to any table where someone requested a well done steak and confirm the order. He also told them he would butterfly the steak to get it cooked to doneness and that’s why it would look different than the other steaks. At the time, I thought it was weird but it did head off any questions.
How do you plan to cook it?
I’ve had poor results from sous vide attempts with seafood. Probably I’m not doing something right, but I’ve had a salmon filet more or less disintegrate out of the bag. It didn’t taste bad, but as for looks, scrambled salmon hash was not what I was trying for.
But I agree that browning salmon isn’t the way to go either; I have had good success cedar planking salmon, as well as shad and even bluefish. You avoid charring the filet, and you get a nice wood-cooked taste even if you’re over propane.
To my mind, there are only three possible faults in sous vide - adjust the temperature, adjust the time, or… make something else instead. 
My plan was to let my brother grill it while I watched netflix.
This makes a lot of sense, especially assuming they cooked all their steaks at quite a high heat. High heat cooking a thick steak till it was well-done inside, would mean the outer two-thirds of the meat would be like leather. As the heat is turned higher, “How far away is the middle of the meat?” becomes a more and more important question.