Yeah, I always wondered too... In the anime, I think I remember seeing the fancy design once? But I don't have time to search for it right now. Though I think they stuck with a plainer design for the anime just to make life easier. If you look at the manga in the first chapter, it's obvious the badge is more ornate than the first link you put up (more shield like and plain) and more like the second one (rounder and more colorful).
In this case, I think the more ornate one just looks nicer. However, this one
is the badge I purchased. It's not super plain looking like the first one you linked, it is more rounded, but not as ornate as the second or third. I made sure to get matching badges for my group (4 of us), even though two of us ended up with different jacket color/material than the other two. XD
I think for cosplays, people tend to favor the fancy ones? I've even seen people embroider their own. All the same general shape and design, but some fancier than others with slightly diff colors. Though I've no idea where the silver and purple came from. I guess your best bet is to choose the one your group will be getting or just choose the one you like best. ^^