Good comicbook antagonists are not just about the hate or the colorful schemes, they can also challenge heroes in different levels, even going as far as to compete with them for similar goals. Instead of being one-sided these polar opposites recognize each other and have some respect for what they mean or stand for.
Since this is a great concept, why not play in rivalries? I thought about some of the most emblematic ones that came to mind (they are different from one another, so maybe you'll find they aren't really rivalries, that's fine, use this thread at your leisure).
Anyways, my picks:
Magneto and Professor X.
Loki and Thor.
Doctor Doom and Reed Richards.
Hercules and Ares.
Sinestro and Hal Jordan.
I wish I had more DC examples in mind but my mind since to be dry
The only antagonists in that list is Magneto/Xavier. Doom and Reed is entirely one-sided since Doom just hates on Reed, Hercules and Ares are gods and cannot be compared or whatsoever, Loki and Thor are just a sibling rivalry gone cosmic and while superior to Hal/Sinestro have a workplace dispute and are not really antagonists so to speak.
A lot of these guys aren't truly villains, at least in recent memory. Loki and Thor work together, Ares was a bona fide Avenger and Magneto was part of the X men
Doom hates Reed, but he also sees him as one of the smartest men he knows, deep down he considers him the only one able to keep up with him and give him a challenge
Herc/Ares and Loki/Thor, per your own words, are a sibling rivalry, totally a rivalry
You just described Hal/Sinestro like a dispute, which is the origin of the very word "antagonist"
But I guess it's my fault for telling you to nitpick me on the OP
Antagonists are people a group of people or institutions that represent the opposition against which the protagonist must contend.
As originally envisioned this is Magneto and the Brotherhood and Xavier and the School for Gifted Youngsters. So, they count.
The operative word in workplace rivalry is rivalry. It comes from the Latin, riv6672.
LOL Hal/Sinestro as "workplace dispute"! Makes it sound like Sinestro was pissed off with Hal because he borrowed his pencil sharpener and forgot to return it!
I honestly wouldn't consider Xavier and Magneto to fit the bill, really. Not always anyway. Their relationship veers wildly from trying to kill each other to homosexual tension at times, so it's hard to classify them properly, imo.
You know, I can't go around pretending I give a sh_t about X-men characters
Again, what's a true villain in this day and age? The kids want to see Sabretooth leading the Avengers and Carnage dating Mary Jane, we cannot disappoint the kids.