I only jumped into E.Y.E. because a friend of mine had purchased it and I felt compelled to join into the co-op. Once I got into it, however, I found it was amazingly deep and complex, especially for a $15 title.
The most direct comparison would probably be the original Deus Ex. It's an FPS with significant RPS trappings. You gain experience for wasting fools and completing objectives, and you spend the experience on abilities which customize your character along either the "stealth", "fighter", or "hacker" lines. There's an infinite number of ways to spec your character, so it doesn't boil down into "classes" as much as it does personal preference.
The gunplay is solid and intense. It's a real pleasure to shoot the guns in E.Y.E.. I'm somewhat of an intensity whore: I like my guns loud, scary, and intimidating. E.Y.E. does a great job with making each gun feel unique and powerful. I'm not the most sneaky player; most of my missions devolve into brutal gunfights, but I don't mind because they're always intense and entertaining.
Your character has access to several special "psychic" abilities, as well. Examples include mind control, cloaking, and summoning. You can switch between gun play and psychic powers easily. You'd don't HAVE to use these abilities to solve each conflict, but they are a welcome addition which add another layer of depth onto the general game-play.
The graphics and the sound are surprisingly sophisticated for a Source engine game. I didn't expect this level of quality from the same engine that ran Half-life 2 nearly 7 years ago.
I can't speak much to the multiplayer/co-op, since I haven't done any yet. It looks like a lot of fun, though, and I can't wait to give it a shot. It looks like it's very fluid "drop-in-drop-out", which is a always a nice touch. There's a lot of missions which really benefit from a co-op partner, and it will be a lot fun coordinating those missions with a friend.
It's not without some problems. The plot and dialogue make absolutely no sense. It's evident that this was translated from some foreign country and clearly took a few hits along the way. The tutorials are nebulous at best and rarely provide any real insight into how the game functions. However, it's worth suffering through to get the excellent game-play. After the first two hours, you will have developed a game-play style which fits you best, and you will be building your character up around it. It's a rare game nowadays that lets you truly customize your game-play experience, and you'd be remiss to let this one slip by unnoticed. The low price tag, the fun combat, the entertaining multiplayer, and in-depth customization make E.Y.E. worth a look.