My take on body armor is that I like to keep the Armor values to 1 or 2.
Concealable vest: Armor 1
body armor worn over clothing: Armor 2
Vest with strike plates: Armor 3
I haven't had anyone ask me about anything greater, but I suppose at Armor 4 you'd be talking Army of Two gear, the kind of full-body coverage that'd let you rob a North Hollywood bank or go on Ghost Recon:Future Soldier missions.
I have also allowed some armor to take a Mild consequence for their wearers, basically being "my armor's ruined!" and doesn't work anymore. I find this works best for archaic armor, shields, and vests with strike plates.
I'm lenient on allowing ballistic armor to work on knives and stabbing weapons (although that's easily defeated with a Declaration about needing a stab vest to stop stabs), although I rule that archaic armor does NOT stop gunfire (unless of course you've got a wife who lines your mail with kevlar and then you bullshit your Declaration well enough that the GM allows it).
To counter that, well, you can aim as a Maneuver (either for the typical +2, which in effect can cancel out Armor:2, or tag for effect to say you're aiming for where there is no armor coverage) or Declare you've got armor-piercing ammo or something. A lot of monstrosities have enough natural hitting power that wearing armor just makes the character in question think they can go toe to toe with something that they'd otherwise engage more indirectly (and smartly). As a result, I really don't have much problem handing out body armor to my PCs. They're all outlaw degenerates anyhow; body armor would be the last thing for which any police would stop them.