One thing White Collar gets absolutely right and very few other shows do, is that people React to guns.
The reaction varies, depending on their level of training/comfort with firearms, but there's no cool guy bravado* when someone pulls a gun, especially not from Neal. When he sees a gun he always always always reacts like things just got very serious, this is no longer fun and games.
And you know what? Yes please. It also ups the stakes for us when a character reacts to someone pulling a gun on them, and it's also highly realistic. I just really appreciate it that guns aren't a prop to signify "antagonist" but a weapon that should and does elicit fear.
* except for when Kate pulled a gun on Peter, and even then his reaction was warranted.