Destiny was a weird one, so much hype, so much expectation and while it didn't live up to that hype or expectation. Destiny was still a pretty good game, all things considered.
A very weak story, with some fairly bland mission objectives couldn't stop what turned out to be a game with some great gameplay mechanics, a semi-interesting loot system and a co-op that still remained fun despite the faults.
The loot, as I mentioned just above, was semi-interesting. The loot system as a whole isn't as good as something like a Borderlands where there's loot drops all the time, all around the place and just copious amounts of stuff to always get. Instead Destiny's loot system surrounded your level and eventually builds up to when you reach level 20, which is where the 'interesting' part comes into it. Basically, your future levelling beyond that 20 comes down to the loot you collect therein. There's no more actual physical levels to go up, you only go higher based on the loot you have. So the incentive in this loot system is done in a really interesting way, meaning you need to keep playing and going for high level risk for high level reward.
But with that loot system, comes the biggest problem with the game. It's easy enough to overlook a bland story and fairly heavily repetitive missions if you have a good system like the above to fall back on. But when that loot system only really comes into it's own once you reach level 20 (and therefore have completed approximately 20+ hours of content, if not the entirety of the base games actual new, fresh content), then something has gone drastically wrong.
And that, along with the flat story and repetitive missions, is where Destiny falls short of the mark of being a great game. The game just misses the mark too many times to be called great. There's plenty of fun to be had, but too many mis-steps along the way as well.