I agree with concrete_angel. You want to show struggle. You'll also want to keep in mind the goal of both the protagonist and antagonist in the scene. One wants to get away; the other wants to catch him.

While it doesn't have to be a gunfight, something along the lines of Catch Me if You Can comes to mind. Slipping by someone unnoticed might be difficult, and when both of them are trying to one-up the other, things move along quickly.

At some point, your bad guy is caught. Guns raise the stakes here, and there is the possibility that the good guy or bad guy won't walk away from the fight or innocent bystanders become collateral damage.

Here is where I stop to brainstorm the good, the bad, and the nearly impossible. Sometimes knowing all possible ways that this capture could go will give you ideas. Gunfight where bad guy dies. Gunfight where good guy dies. Gunfight where someone else dies. Cornered without gun for good guy. Sneaks by good guy without being seen. Accidentally trips over something stupid while sneaking by and gets caught with gun in face.

I don't know which way is the best, but there are a million possibilities.