Ok, so I have played both EVE and Elite: Dangerous. As someone who loved Freelancer, both disappoint.
EVE is true to being an MMO, monthly subscription, steep learning curve, figuratively and literally. The game can be a lot of fun, but it has a slow start. Make sure to join an active corporation, or it will get boring very quick, it is like all MMOs, it is a lot more fun if you play with people you know, or get to know. Some corporations will help you a lot when you are new. Now EVE can pull you in heavily, it did it to me, hehe. It is pretty addictive, but it can go slow later on, especially if you play solo.
Now Elite, it is a beautiful game, but I got bored after a while, as it is difficult to group up with people, obviously later this was kinda fixed with the Wings update, but it wasn't enough for me. Basically the game looks great, plays great, but after a while trading, bounty hunting, missions, exploring, etc. gets boring as it is all procedurally generated, meaning that after while things kinda start looking the same. IT also sometimes feel like a grind if you want to get specific items, as they are expensive. Now I did play this game before the new expansion, played it al launch.
Now this is kind off a negative review of both, just to show you that there is a negative side to both. Though I am getting to the point where I can't play MMOs any more as I get bored very quickly, as I am not as intrigued by the story like I am with single player games. So take this review with a pinch of salt.
Though if you ever want to play a great space game, try Freelancer, it is a 2003 game, so it is pretty old, the people who are making Star Citizen made Freelancer back in the day for Microsoft. Though there are no more official measures to get this game, so you'll have to find a download somewhere. The game is old and some of the mechanics you can feel it, but overall it was a great game.
EDIT: Also if you go for Elite, check up keyboard/mouse key setups, I changed mine, as the mouse controls are weird as hell.
For example throttle on my mouse wheel, mouse left/right as yaw and not roll, as that is confusing as hell, I put my up down thrusters on W and S, A and D for left and right, Q and E for roll. That covers almost everything, just remember Elite doesn't like yaw, so roll and then turn by going up or down.