Fallen should be climbing up the side of walls and shooting at us, they do have the ability. Although, with the gravity on our planet versus where they are from could be a good excuse, but on the flip side...don't call their pwnge walker the "Spider" after a bug that can climb walls....if it can't climb walls.
The hive use darkness to shield themselves, and The Fallen use their technology as a scavenger warrior race. The Fallen's bullets can partially trace you around, where the Hive's bullets are more direct, faster, but hit for about the same. They can fire faster. When you actually observe their "mannerisms" you will notice these small things. There is probably another race of Fallen we have not seen that can fly or climb, same for The Hive and future enemies.
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It's called a Devil Walker. They also have a "Guardian" name of Spider Tank.
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Sorry, somewhere in between I swear they called it a Spider but you are right sir