Considering both games aren't out yet I can only go on what I've read or seen in videos etc, so some of this may be old hat and subject to change before they're released, but this overall summary and conclusion is my own personal opinion on how I think both games will be perceived - so don't take it as gospel, a lot of it could be way off and change radically before release dates !
I think the main differences are about the way both games have approached their respective
depths of gameplay.
Star Citizen:
I envision SC will offer the player more depth of gameplay within your avatars immediate surroundings and the effect your avatar can have on it via hands-on interaction. For example, from the off you won't be confined to a cockpit seat. You can interact with your ship, walk in hangers and spaceports and possibly planet-side too, you can drive land vehicles, and I've even heard mentioned the possibility to go EVA to repair your ship (not 100% sure about that yet), from various fan videos I heard you can board other peoples ships and help fly them, or even board them aggressively in an attempt to hijack/steal them. You can effect the SC economy as its player driven. Combat is a big thing in SC. You can start off in a mission-driven military environment, or be a civilian making your own way. Exploration-wise you're limited in scope since the SC gameworld only has around 100 systems - although this will be expanded upon in further releases. And those systems won't have realistic motion so I'd consider them background eye-candy if they serve no real interactive purpose (I stand to be corrected on this though :smilie

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Unless its changed, death in SC will have meaning in a sense that it will reflect on how your avatar will look to other players. The more you die the older and more physically scarred you'll appear. You'll be able to see the difference between veteran players and rookie players from appearance alone. You will only have so many lives too before your character is killed off forever - whereupon all his wealth is passed on to your beneficiary. So your character(s) have a finite lifespan. No Eve-style immortality via clones. -
I've only seen this aspect mentioned once so am not sure if that is still the case in regards to death in SC.
I can see SC being an exciting and chaotic place to play due to the massive playerbase it'll have, especially since that playerbase will be confined to a 100-system gameworld on release.
Elite Dangerous:
Elite Dangerous' depth comes from its wider environment and the career paths one can take within it. In ED you're just a small cog in an infinite machine (as has been mentioned on here a few times). The galaxy will have realistic celestial mechanics and 400 billion destinations to choose from. Star systems will have real value from strategic, economy, and exploration viewpoints. They will be fully interactive with seamless landings in expansion 1 or 2.
Initially you are your ship since there is no external walking on release. I doubt your effect on the economy will be like anything SC has to offer since its in the main AI-run. Death in ED is meaningless from a non-financial viewpoint.. as in you only lose out financially (ship, cargo, equipment), possibly a bit of rep too, but there is no permanent death (except in ED's version of Ironman mode).
ED gameplay will on the whole be more sedate from a PvP point of view due to its sheer size and grouping mechanics where you can get lost in 400,000,000,000 systems and never see another player, or simply switch to solo group if you don't feel like meeting anyone while you're out doing what you do. In that sense the game could appeal more to adventurers than it will to PvPers.
In a very very very basic nutshell I see SC being akin to a shoot 'em up in space with a touch of adventuring thrown in, while ED will be a limitless space adventure, with combat there if you seek it.
I only backed ED but I'll be an avid player of both!