I haaaaated borderlands. Absolutely despised it. OTOH I loved destiny beta after not expecting to enjoy it. Went from 3/10 meh to 9.5/10 can't wait day zero buy.
I didn't like borderlands either. Mostly because the game felt lifeless to me. I guess it was the landscape, it felt empty and hollow at times. I am also not a big fan of cel shading in games though.
I think the online world where you can meet up with random people and participate in public events in Destiny really works. It removes the linearity of most shooters and opens up the game world for the player, rewarding your exploration. It definitely has bigger landscapes than borderlands and is more open world.
The alpha explore map was huge and didn't have any loading, it was all seamlessly accessible. There were multiple locations to explore in the alpha test that had no loading between them.