If there are two more aggressive garden birds in this part of the world, I have no idea what the might be. All garden birds are a little aggressive to other birds. Some birds, though, when they hit the feeder the other birds decide there’s a branch they’d like to visit elsewhere.
All woodpeckers are aggressive — not based on their size. They are aware that they have very thick skulls to go with their deadly beak, so even bigger birds avoid them. Some of the smaller ones are more aggressive than the bigger ones.
Blue Jays are aggressive. They attack the nests of other birds and eat or destroy their eggs. And if you get near a nest, don’t be surprised to have a phalanx of Blue Jays attacking you. They don’t mess around.
So it figures when both landed on the same feeder, it was eyeball-to-eyeball and neither backed down. They flew off together.