In one shot, he totals the invincible car, and Fury is forced to make a desperate and cartoonish escape into a hole in the ground -- a getaway so ridiculous that the Winter Soldier never even considers pursuing him. Though in hindsight, it probably should have occurred to him that a super soldier could have caught up to an injured man in a tunnel with a four-second head start.
So this organization has their own super soldier who happens to own the only gun capable of taking out their target's impenetrable vehicle, and he's only there in case their first two bumbling plans fail? Why not start with the Winter Soldier? Why not simply track and snipe Fury when he's walking to his car? And before you say that's a dull, anti-climactic way to kill someone in a superhero movie, remember it's exactly what happens in the next scene, in which the Winter Soldier easily tracks and snipes Fury.
In a classic spy move, Nick takes a drug which lowers his body functions to fake his own death. So Hydra, after spending all day and the lives of many deep undercover operatives to kill Nick Fury, still gets fooled by the oldest trick in the comic book. This is probably the most important step in their entire 70-year conspiracy, and they put less thought into it than a Taco Bell chef unveiling his latest arrangement of tortillas and cheese sauces.
"I can't believe I ever sided with these guys."