Warwick is designed to do consistent damage. Shaco is designed to burst. If shaco doesnt have the damage to 100-0 his target instantly then he usually loses the fight.
Warwick is all about slapping you down for a while. So it would make sense that he is better at fighting than a shaco. Not to mention built in lifesteal means he is designed for drawn out fights.
So even if the warwick is behind, if the Urgot hasnt built in a way that he kills warwick quickly, warwick will most likely just out sustain the damage and kill him.
They key to kill warwick is burst. All sustain champs like him win extended fights, as that is their design purpose, but they give up burst.
Warwick has 1 damage ability outside of his ult. He literally just slaps you and occasionally chomps you. This means he has no burst, But Due to innate lifesteal and Q healing he is the king of extended brawls.