Both Angel Beats and The Melancholy of Haruhi Suzumiya feature a strong female lead as well as a "brigade." In Angel Beats, there is the SSS Brigade, and in Haruhi there is the SOS Brigade. Since Haruhi came first, is it possible that Angel Beats copied Haruhi?
tl;dr - They share what literary types call "themes". Angel Beats and Haruhi are both "school anime", so they will more than likely share themes.
School anime is a theme, the "school club" and "strong female lead" are also themes. You will find these themes in many anime as you watch more of them. Another example of a "school anime" with a "strong female lead" that's president of a "school club" is Medaka Box.
I wouldn't say Medaka Box copied Haruhi or Angel Beats, though. Just as I wouldn't say Angel Beats copied Haruhi.
Probably, since the main girl in Angel Beats (can't remember her name) is pretty much just as annoying and bossy as Haruhi. Both animes also take place in high school and have loads of weird situations, so that makes them similar. I watched both shows a while back, but from memory, I don't think Angel Beats straight up copied Melancholy, but it probably took a lot of inspiration from it. The author might have been like, "Well, Melancholy is really popular, and especially the main character, Haruhi, so I might want to make my story a little bit like that so it'll sell..."