Sorry for double post, but Star Citizen is centered (Not entirely though) around the online aspects of space sims. X Rebirth is a hardcore singleplayer only thing.
So in terms of instancing, there is none of that in X Rebirth and the battles have no limit in size unlike Star Citizen (You could have dozens of cap ships and hundreds of fighters with little lag, due to the way they have optimised the game cleverly. It now only supports 64bit - huzzah!), while on Star Citizen the player cap will be 100 or so players per instance, which inevitably means less ships.
X Rebirth provides a lot of fun and very engaging plots, that give you things like a Player HQ, special/prototype ships, which lets you build your own ships and outfit them etc. While Star Citizen has one campaign (On release, there will be more) that gives you some credits and MAY, depending how well you do, give you citizenship in the game's universe - which gives other benefits.
Other than that, they are both do whatever the hell you feel like games, with a lot of content and potential.
EDIT: Gonna preorder X Rebirth tomorrow, yay. Can't wait for the Star Citizen hanger module in 3 days either. This has been a great year for the sci-fi genre.