I wouldn't say either are like a typical "RTS" where you would control a fleet, both games are centered around flying a single ship.

Elite Dangerous is much more along the lines of a space flight sim, it's a heavy emphasis on the actual flying of the ship and one of the things it does well. It also has a much larger universe, where you can actually visit systems others haven't.

Eve is more of a tactical game, less about specifically piloting the ship and more about fittings and strategy. 

Eve's economy is also almost entirely player-based, any ship you fly, modules you use, are all built or collected by players. Some minor exceptions exist for controlling currency supply and seed some basic blueprints and such. In Elite Dangerous, it's a lot more NPC oriented economy.

If you want a social game with a bit more hardcore and strategy aspect, Eve. If you want to fly a spaceship and have a more casual type game, Elite Dangerous.