Ultimately you can spend a whole night trying to find fights in Eve and get 2 or 3 fights that last 20 seconds.
Or you can play 10 matches of overwatch or CS:Go or DOTA that last 30 minutes in the same time.
It still doesn't have a decent competitor though, elite dangerous is rubbish, still waiting on Star Citizen.
Longinius Spear once quoted Ernest Hemmingway, in a presentation at Eve: Vegas, "There is no hunting like the hunting of man, and those who have hunted armed men long enough and liked it, never care for anything else thereafter."
Edit: Actually I prefer this response: I think how true an EVE player finds the above statement is a good indicator of how effectively they played the game to begin with.
Personally I think that if you believe that you're still in the delusion phase where you're projecting your fantasy of what playing Eve should be like, compared to what playing Eve is actually like. That fantasy lasted a long time for me, like 3/4 years.
In reality battles are copying someone's prescribed fit, click a direction to align, letting your squad leader warp you. Eventually you might actually get a fight, which consists entirely of clicking the first name on an alphabetically sorted list and pressing F1. There's no skill, only the adrenaline rush of losing something you spent 2 weeks grinding for.
And don't forget, you spend 2 hours or even days between each of these battles waiting to even start the fight.
The big contradiction in Eve is that the thrill comes from permadeath, but it's only a thrill because the grinding is onerous. If everyone had infinite isk, no-one would play it because the fundamental combat gameplay is super boring.
If you want the kind of rigid corp structure EVE offers but in a high-action game, I'd say look at some of the dedicated ArmA groups; particularly ShackTac.
The combat side of EVE is best played as more of a situation room. Sit and monitor comms and see what's going on over a wide area of space (read a book or do something engaging while you do this), then plan a surgical strike, execute and get out.
EVE is a role playing game - you play the role _you_ want to play! You live a life in EVE, as though you might live a life in the real world. You choose to trust people and make friends, may be get betrayed, or do the betraying yourself.
You fight an enemy because he/she is trying to steal your stuff, or take over an area that you want to keep owning.
Even though eSports games have more action, it's not the same kind of thing, and there's less thrill because losses in eSports are temporary. There's always a next game. Losses in EVE feels real, because they _are_ real!