Lord Corax is the Primarch of the Raven Guard, and the liberator of Kiavahr. In his background, he is portrayed as a stealthy person; he discovered in his "childhood" that he can be "invisible" even when in plain sight of others. This is repeated in several Black Library novels. In other ways, his childhood is somewhat disturbingly parallel to Konrad Curze of the Night Lords, in so much as he grew up in an oppressed world full of villainy. The key difference seems to be that instead of being a loner who brought peace to a planet, he was brought up by a large variety of people he moved between (or was shuffled between) and learnt from them. He kept in touch with his humanity and was able to forgive murderers such as Kaedes Nex eventually and use them in the rebellion and later in part of the Raven Guard.
In other ways, his leadership is perhaps analogous of Alpharius of the Alpha Legion. At least in so far as he councils his sons to think for themselves and be adept with hit and run tactics, infiltration, and decapitation strikes. His legion is not as flexible as the Alphas, but this is only because they concentrate on honing their quick strikes from the shadows, rather than combined arts warfare.
Firstly, it is important to note that Corax is an army wide booster. He not only gives his sons acute senses whilst he is on the board (I've no idea why this would be the case in terms of the background?), but he also gives them the ability to run the maximum distance all the time when he is on the board. This is a real boost for Raven Guard armies that are foot-slogging across the battle field and can certainly make up for the otherwise slow moving components of their troops.
As The Shadowed Lord, Corax can only have snap shots taken against him by anything short of daemons and psykers if he is not their closest target. I really genuinely like this rule. It means that he should be played as a single person who does not join a unit, but instead stalks the battlefield looking for he prey. It also harkens back to 4th edition where units had to take Ld tests for target priority (a rule I also was very fond of). But more than this, it means that he cannot be hit with flame or blast templates. As if this was not enough, if he gets in to a tight spot or a bit of a pickle he cannot win, he can just vanish and be placed in to ongoing reserves (so long as he's got the higher initiative, which he should most of the time).
His melee weapon gives him some tactical flexibility as every turn he can select between having some extra attacks, and other bonuses depending on whether he wants to rage at an individual, or avoid the mass of arms that a horde could bring. His armour is 2+/5+ with a deep strike disrupting ability to boot.
Depending on which version of him is being played, he'll either have some archeotech pistols, or a heavy bolter (that he wields as assault 3). Plus, he may or may not have his jump pack that can provide better hammer of wrath moves and vector striking.
The player can select between two modes of Corax, 100 points apart from one another. The worse one is the one without the jump pack and with the heavy bolter. This is to represent him in action after Isstvan V's events. If you're given the option and you're not playing fluffily, take the more expensive version. The jump pack is amazing with Corax and he is a literal monster with it.
I see his primary negative being his large points cost coupled with only a 5+ invulnerable save. He is really not going to like thunder hammer terminators and the like -- that invulnerable save makes Corax poor at soaking up incoming damage, unlike some of his brothers. You'd think Mars could have created something better for him.
Overall though, he's totally worth his cost. But he must be played wisely. Select the targets carefully, go to them and annihilate them, before moving on to the next target. And the next. And the one after.