I'm sorry but the grinding in Destiny is way worse because there is a lot less content.
In Borderlands you can play through the game maybe twice and hit max level and get some very interesting guns(even if they aren't legendary). Destiny makes you play the same content over and over again. Seriously there's a bounty requiring you to do 25 strikes to get an exotic weapon. There's only 4 different strikes (5 for playstation users). I've found many people who could actually come up with 5 good reasons so yes I do believe it's reasonable(hooray for opinions) for people to like Destiny over borderlands. I just think your same amount of grinding reason is just downright wrong.[spoiler]i like destiny too[/spoiler][spoiler]i love borderlands[/spoiler]
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Truthfully I haven't played the pre-sequel. Borderlands gives you more loot, but most of it isn't useful. You do grind, maybe not for better loot, but the boss fights are a grind. [spoiler]I really liked Borderlands, had fun with Borderlands 2 until it became boring for me.[/spoiler]
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Boss fights in borderlands are fun and don't feel as scripted as destiny so I don't really consider them a grind