CO-OP:
Destiny feels like it has better designed non-boss encounters and is less likely to devolve into needing an ally to revive you every thirty seconds. It's Halo-esque in the sense that you have AI capable of surprising and sometimes challenging you, rather than just charging straight at your face every time. The boss battles, however, seem iffy. The Devil Walker in the strike included in the beta sent me right back to Borderlands where people were getting one-shotted left and right and we had to restart the entire encounter numerous times.
On the other hand, I prefer the 4-player co-op of Borderlands to Destiny's 3-player fireteams, and BL actually seems like its abilities have more interesting co-op implications, like Maya in BL2 being able to resurrect allies at a distance, heal people by shooting them, or give everyone a health bonus for killing a Phase Locked enemy. Some of the sloppier elements of its design make it more of a "drinking beers and cracking jokes the whole time" co-op experience than a "tightly gripping your controller, completely fixated on the game" one, but there's room for both.
LOOT:
Mostly a matter of quality vs. quantity here. Destiny's items are fairly similar to the Guild Wars series in that they'll fall into one of several basic templates, with their stats being determined by their type, level requirement, and rarity. The approach of needing to level weapons up before you can use their special abilities is interesting, but the fact that there's no difference from a stock weapon initially is kind of disappointing.
Borderlands prides itself on being extravagant with loot. To me, that results in higher highs and lower lows, as the RNG gods are capable of giving you something much more unique and powerful than a weapon in Destiny where you're basically limited to one affix and a single selectable option. (At least with the uncommon items in Beta.)
CHARACTER DEVELOPMENT
Destiny wins for giving us access to more abilities, but it seems like the individual options available
within each sub-class are less transformative than BL2's one-point wonders that can dramatically change the way your class is played. No conclusions here, I have to reserve judgment until I play the full version of Destiny.
PvP:
Really not sure how to feel about Destiny's PvP just yet. Time to kill is a little short for my tastes, vehicles are completely dominant when available, and many entire weapon categories seem to be completely useless. If the retail version addresses some of these things, I could find myself spending a decent amount of time in the Crucible, but it's hard to say.
STORY/WORLD
I like them both for very different reasons but I don't feel this is a major factor in me preferring one to the other.
MISC:
Destiny needs to work on some of its convenience features. Needing to go to orbit, re-select The Tower as my destination, then wait through another loading screen just to turn my encrypted engrams into items is a real pain.
My overall conclusion is basically this:
Bottom line is that there is room for both games. Totally see myself playing Presequel on PC and Destiny on PS4 this year.
BL and Destiny are both great. I love co-op action-RPG-shooters and it'd be great to see even more games in this sub-genre.
