I played it for a year or so, starting near the bottom of the complexity rung (flying around in ships with a USD value of something like 1 cent, shooting AI-driven space pirates) and moving up to piloting one of the largest available ships in the game (A 'Supercarrier', which essentially acts as a huge mobile support vessel with the ability to deploy fighters - with a real-world USD value of probably around $500). I was playing in one of the largest player-run alliances in the game at the time - we had a section of space carved out that we shared with various allies and fought regularly to defend.

The game is definitely full of time-sink complexity: Resources used for construction in EVE only come from a few sources, all of which are directly or indirectly player-driven - if you want to get raw materials to manufacture things, you have to either get them by mining asteroids (manually), killing AI-driven pirates and melting their wreckage down for scrap (manually) or by maintaining a setup of 'planetary interaction' stations that harvest resources from in-game planets.

On the other hand, the actual space combat - which is still a cornerstone of the game even if it's very abstract and strange to the casual observer - is often extremely engaging, has lots of room for high level tactics and coordination, and can actually handle groups of thousands of players all competing for control over a single star system. There's nothing else like it.

The best way to describe it is sort of like playing chess in outer space: Every action you decide on needs to try to anticipate your opponents' reactions and you need to apply that level of tactical thinking a few steps out. Likewise, in general fleets and vessels in EVE cannot move very quickly and battles can often become very drawn out, with much of the actual victories and losses occurring in a purely tactical sense (poor decisionmaking, incorrect information from your scouts, poorly chosen positions for your fleet, etc).

One of the other interesting things about EVE is that at a high level, the design team tries to make it a game full of balances and counterbalances. Even once you've 'made it' and acquired one of the biggest, most powerful vessels in the game, you have dramatic weaknesses - a pilot in a supercarrier worth $500 USD can, despite his mighty defenses and arsenal of fighters and point-defense weapons, be undone by a single opposing player in a ship that is literally worth nothing. The way it essentially works is that the smallest, weakest vessels are dramatically more agile, which (as an extension of the game's physics model) makes it impossible for huge, slow-moving, heavy-hitting vessels and weapons to cope with them. The end result is that a viable fleet for combat in EVE needs to contain a mix of cheap, disposable vessels (to confront and 'tackle' the opposing fleet's big supercarriers and other heavy-hitters) along with a mix of larger, more expensive vessels to do the work of actually dealing damage to opponents and providing logistics support (scanning, repairs, etc) to the rest of the fleet. It creates a really nice equilibrium where, when the game is working right, new players end up being just as important as veteran players.

On the other hand, arguably EVE's biggest problem is that it is 'appointment gaming' at its worst. As an active player, you will spend probably close to 95% of your in-game time waiting for something interesting to happen. There are lots of things to do to fill that time, but none of them are particularly interesting; they're all preludes to that huge, pitched space battle that (if you're lucky) might happen every few days, if you're awake and around to participate. For people with flexible schedules it ends up being a great fit, but for me, it was hard to fit into my schedule and I ended up with few opportunities to participate in the 'fun stuff', so I ended up giving my accounts and ships away to other people who would actively use them.