Each weapon type in Umbrella Corps has its own features.
In turn these are: more damage on headshots, less damage at long range, and more damage at close range.
Certain weapons have a piercing ability that allows them to shoot through zombies (zombies that are shot are shown with a blue-white effect).
Your movement speed is also affected by your weapon, from fastest to slowest these are:
Brainers > Handguns > PDWs > Shotguns
Remember to swap weapons if you need to sprint faster, for instance switch to the Brainer if you need to make a quick escape.
Make sure to check the customize screen for further details on each weapon's abilities so you can find your perfect match.