The most prominent new items you can equip to your cop or criminal are stun guns, gas masks, blunt melee weapons, gas grenades, grappling hooks, and ziplines. Most of these items are fairly self explanatory, and when you use them by themselves you don't really get much out of them. It's when you combine multiple items that things start to get interesting.
For example, equipping your Operator with an ammo bag, gas grenades, and a gas mask lets you flood enemy defensive areas with an unlimited number of vision clouding, accuracy-screwing gas canisters--making opponents easy kills in the maps' chokepoints. Stun guns, blunt weapons, and grappling hooks make it easier to sneak up on perching snipers. Just shoot a hook up a ledge behind the sniper, climb up, and incapacitate them with a stun gun or police baton. Interestingly, you're then free to interrogate them (which gives you their allies' locations).