One thing a particle cannon would be especially good for is intercepting missiles. This is because a particle beam is more or less a direct-fire weapon, that is, you just point and shoot, no need to compensate for target motion. This is much easier than current solutions to missile interception, such as Phalanx, Goalkeeper and DARDO, which fling hundreds of bullets in a very short period of time (100 rounds/sec or so).
The direct-fire aspect of a particle beam would likely make them the weapon of choice (along with laser cannons) for killing starships at a distance. While missiles and mass-driven kinetic slugs might do more damage, a ship at a long distance could easily dodge a slug or shoot down a missile.