Let's make a few comparison here. And I'll be as unbiased as possible for once:

There's 3 things that make up the most important elements of gaming: Gameplay, Story, Emersion. They define as such:

Gameplay: Systems the player uses to interact with the game to bring meaning.

Story: Gives reasoning and logic behind actions

Emersion: Combines Gameplay and Story to create the reasoning for continuing forward.

Now on gameplay, Destiny wins hands down - it having the addition of PvE gives it more to do then simply smashing anothers face in. How it actually plays is almost identical. If you're good at one game - you'll be good at the other. So the lack of something other then PvP or modes for PvP gives Destiny the edge.

Story, both fail miserably, but at least Destiny tries. Dust has nothing to bring someone into the world of EvE - you can read all the item descriptions, but you'll only get a feel for the game - the lore can only be found online or in a book. Where as Destiny's lore can be found in-game, though through troubling means. Destiny, also, at least attempts a story, regardless of how bad it turned out. So in Dust - you're basically aimlessly running around trying to figure out what to do next, where as Destiny follows a plot-line. But events in Destiny are so dry, and rivalry in Dust between the lore being so intense it carries on to players, it's obvious which story reigns supreme.

Emersion, Dust wins. There's a community here that reaches out to each other to do things and create content for ourselves. Destiny has nothing outside what the game itself delivers, which is a very limited, and likely never will, as player size per map is tiny.

over-all Dust is a the better game in almost every field but the one that matters most to people - gameplay.
But this could easily change in 3 months time - as Destiny has real funding and a team behind it to deliver possibly amazing content, where as Dust is a dead fish in the water.