I'm not 100% sure what you mean by "longbow" stance. I've seen people get into about every position possible to shoot. The bottom line is to you whatever stance enables you to hit what you are looking at most consistently. Having said this here is a reason for standing different.
Recurves are centershot so you can stand erect and get good alignment for shooting. The most erect and properly aligned are generally the olympic shooter and field archers. Before the modern longbows became popular most longbows were not centershot. Almost all selfbows are not centershot. When the bow is not centershot the arrow has to bend around the bow and go through archer's paradox. Unless you are shooting a very heavy bow it's hard to find weak enough spined arrows to get tuned so most folks tend to hit left. So what they do is cant the bow. They are essentially changing the plane in which archer's paradox takes place - making it more vertical vs. horizontal.
They also tend to bend at the waist. The bottom line is that no one will say, "you're not using the right stance" when you shoot the 12 ring on a target. It simply doesn't matter, BUT I will tell you that the most important thing is to use a stance that is easy for you to replicate time and time again. When people change their stance many of them don't realize that they often change their draw length. If they open up they tend to short draw thus causing the arrow to shoot low. This is what gives them problems on the 3d range when their foot is on the stake and they are forced to alter the stance.
Good luck in choosing what works best for you. Happy shooting.