I did not forget about it as he has to use the Passive befor Urgot W. Like I said skill matchup. If your W is after your debuffed, odds are he has slapped you around already with 1-2 Qs, and got his W off, at which point you took 2-3 abilitys of damage AND his passive and likely your shields not even gonna stop that 3rd Q befor breaking.
The passive damage is reduced by the shield if its up, and it does not affect the shield amount if its already been cast.
Casting W after being hit by trox passive, This is not blocking damage well. Ideally its if you see the first Q sweet spot about to land you pop W, Then E to get out of his follow up or E into him if you have his hp low enough that you can attempt a full Leg guns and R kill.
So again, id give urgot the slight advantage in a balanced skill matchup, just has more opportunists to win trades or get free damage off but I think aatrox has much better synergy on ganks. urgot 2v1 struggles, aatrox 2v1 struggles but his R can give him a better window. in 2v2 Aatrox has better AOE, better CC and can be difficult to focus cuz hes just going to Rez .
Edit So I very much disagree with frontline Fury. But I don't think aatrox inherently wins lane vs urgot and its gonna be decided by the players more then the champions. And in equal skill, not counting for jungle or mid impact, id give Urgot a slight advantage due to range and slightly stronger mid game as a lot of his kits power spikes are off EXP helping his passive.