Former cop here: I think the biggest misconception about SWAT teams is that what makes them different is that they carry rifles instead of handguns. (In fact, in most departments every officer carries a rifle in his/her patrol car.)

A SWAT team is a group of officers who train as a team for high-risk situations like drug warrants and, yes, hostage situations. By contrast, most other officers are trained to respond solo or in pairs, and often don't spend nearly as much time practicing things like room clearance. If the police are going to break down your door, you want the best-trained most experienced officers doing it. The SWAT guys are calmer, more professional, and less likely to pull the trigger when startled.