Crysis 3 was apparently a commercial failure for EA as it did not manage to meet the company's sales expectations. The same happened to Dead Space 3, released in the same month. The latter failing to sell enough copies I can sort of understand due to the micro-transaction debacle. But Crysis 3 I liked quite a bit. I think it is a very entertaining sci-fi first person shooter.
My playstyle was mostly a stealthy one and most of the time I used the upgrades supporting it. I did prepare for possible boss fights by picking the ones giving boosts to defenses and whatnot, too, but I never got to improve them. (Each upgrade becomes stronger when a certain condition is met while it is active, e.g. staying stealthed near an enemy for a certain duration.)
I think playing Crysis 3 as a stealth game is almost a must at the highest, post-human warrior, difficulty that I again chose to continue my tradition with the series. The checkpoint saving system introduced in the previous game is still there and combined with deadly enemies, one ends up replaying some parts a few times. It gets annoying if you clear a pack of enemies without issues but later do some silly mistake and a single opponent manages to kill you before the next checkpoint.
I eventually gave up on trying the boss on my own. I felt like there was some trick I was missing. I started watching a video of someone playing when the answer finally came to me -- the problem was ditching the Ceph weapon after the suit's overcharge had ended. For some reason I had not quite put it together that the gun would recharge when using a Ceph battery again. With it, killing the Ceph Alpha was much easier, although it did still kill me once with the somewhat randomly connecting slam attack.
The end of the game tricked me a bit -- "Wow, is it really going to have a sad ending?" -- but then you actually get to shoot with a damn satellite at the coming aliens and save the world. And you even survive the fall back to Earth. The nanosuit sure is powerful.
The maps in Crysis 3 tend to be less linear than in Crysis 2 to answer the criticism. Oddly enough, they still often have similar sniper's nests at the entry point where enemies have hard or impossible time getting to. Their grenades can be easily evaded but often that is not even needed as they throw them at walls, sometimes even killing themselves in the process.
Some of the spawn triggers can be immersion breaking, like a patrol of Cephs appearing right in front of you when approaching an objective. One of the first areas also has a room where reinforcements spawn after you have been spotted. Of course that does not happen if you are in the room -- they wait until you leave and then appear behind your back, even if you have killed every other enemy in the map.
I also really liked Crysis 3's story and the characters. Having a voiced protagonist, reborn-in-the-suit Prophet, of course helped but even better is Psycho who returns from Crysis: Warhead. His suit has been ripped from him and he does not seem to like the fact at all. You even get to see a scene of him getting back at the guys responsible for it after the incredibly long end credits -- I swear the Crytek people were all listed twice in there.