Destiny Beta on 360 is pretty neat. It's like a cross of Halo, Mass Effect, and Border Lands. Graphics weren't great on the 360, but that could be due to the Beta or just that it's also on the Xbox One and PS4, so they scaled back on graphics for the 360.
I like how it's open world; you don't have to be in a story-line mission to explore, defeat enemies, and find loot. Oh yeah, loot! I like how you can find weapons and gear in the world and you can also find stuff you can exchange at the Tower for items. Additionally, items you find and upgrade can be used in the multiplier mode. I only played a few matches because you have to get up to a level 5 before you can play multiplayer (level 8 is max for beta) and my time was short. It was very Halo-like, but different enough to be interesting again.
Sorta like an MMO, you'll see other gamers running around on their own quests. You can help them out and even do community events. Unlike a true MMO, you'll only have a finite number of gamers in your world.
Anyway, I'm pretty excited for the full release of Destiny. It seems to be a good mix of campaign, side quests, and multiplayer.