Borderlands has more than 4 different enemies, all of which had reactive dialogue, and at least they hide the respawning by not doing it until you leave the area. You walk around the corner and back in Destiny and the same three grunting aliens you killed thirty seconds ago are standing there again, just hanging out around some boxes, not doing anything.
Borderlands has an actual personality, whether you like that personality or not. Bungie threw a wallet at Peter Dinklage and still had to run his shit through a vocalizer to muffle his bored yawns.
Borderlands gave you a huge amount of content in the base game, and each DLC had distinctly different areas and was as long as most SP retail campaigns. Destiny has vast empty areas in a bare bones main game that they obviously plan to populate for $20 a pop.
Borderlands starts dropping fire/electric/explosive guns out of dead enemies in the first fifteen minutes of the game. Destiny gives you a handful of little glowing cubes you can spend on better guns, once you've collected enough.
Borderlands has loot chests spaced about every twenty feet. You might find a chest or two in Destiny, which will give you an extra copy of a gun you're already using, if you're lucky. And some cubes.
So, yeah, they're pretty different.
