What always stood out to me in their rivalry is that there's really no symbolism to emphasize upon:
Physically powerful Superman vs. politically powerful Lex Luthor
Serious and brooding Batman vs. wacky and random Joker
Righteous and loyal Captain America vs. vile and unscrupulous Red Skull
Lawful Daredevil dressed up as a devil vs. corrupted Kingpin with a good public image
Quipping Spider-Man vs. laughing Green Goblin?
See? It's clear Goblin's original design was random, and there's virtually zero connection to draw between spiders and goblins. Not that it makes their rivalry bad, but it just makes it harder to write convincingly, since there's no apparent deeper meaning you can latch onto like with the cases I listed. So nowadays it's often just GWEN REEEEEEEEEEEEEEE.