Anyone who's seen Breaking Bad should know the answer, this is a fact not a guess, the reason why Hank throws the grill into the river was because it was a constant reminder of how close he came to death, and how scared he was in the beginning of this scene.
He approached Tuco as if he was Jesse Pinkman walking all cocky "Mr. Pinkman", he says with a smile on his face but then when he found out it who it was, s*** got real pretty quick, he turned that frown upside down because he knew how dangerous Tuco was and Tuco didn't even have a gun in his hands and he was already wearing a bullet in his stomach.
Hank, on the other hand, did have a gun on him but he was still shittin'. Hank's whole career he has the backup; his partner and his Squad of DEA soldiers that's why he always act so badass and tough because he basically has a military backing him up as he chases down skinny weak little meth heads, because in Albuquerque that's all there is, it's not hard up there. That gunfight he went through was a real traumatic day in his life, it was the first time shit ever got real and he couldn't handle it that's why when he got promoted to go to El Paso he knew that's where the real gangsters were, and he started having panic attacks, he couldn't handle it and that's why he got into a fight at the bar. He was trying to toughen himself up, he was embarrassed and ashamed that he really wasn't the tough guy he thought he was.
I can't tell you how many hints and clues there are in scenes where they straight out reveal this out right, when Skyler asks Marie how's Hank doing after the gunfight Marie replies you know Hank he's indestructible or something like that, this is a no-brainer I can go hours explaining evidence that supports this fact.