There's technically three types of powers in Mass Effect: Active Powers, Grenades and Passive Abilities.
Active powers a single Global Cooldown. A skill either activates the Global Cooldown or it doesn't. Skills that don't activate a cooldown are only limited by how quickly you can perform the action (the time it takes to switch ammo/throw a grenade).
Most powers listed as a base power here qualify as Active. These are your standard attacks and always cause a cooldown.
Passive powers are always active and don't have cooldowns, simple enough. Ammo powers are technically passive, and you can always switch ammo regardless of cooldown. Tech Armor is basically a passive power unless you detonate it.
Grenades don't use a cooldown either, and if something seems like an "active" power and it doesn't activate the cooldown, that's because it's technically a grenade. Proximity mines, Nova and Sentry Turrets are all technically grenades.
Nova has a "cooldown" that's actually based on your Biotic Barrier (the purple "shield" Vanguards have). You can't use Nova if your Biotic Barrier is empty, but it otherwise ignores cooldowns like a grenade.
A lot of this is dependent on class. As a Vanguard for example, you'll probably never want to use an Assault Rifle - they're just too heavy, and as a Soldier, you'll usually give SMG's a pass - everything they can do an AR does better. Meanwhile, an Infiltrator gets lots of bonuses when using their trusty Sniper Rifle, evening if irresponsibly shooting it from the hip.
The second consideration is range: at very long ranges, a Sniper Rifle offers top notch accuracy. AR's and Pistols Can be pretty good. SMG's can be flaky though, and shotguns are nigh useless. By contrast, Shotgubs ate devastating at short range, but the loss of peripheral vision while looking down that sniper scope can get you killed.
The next consideration is the defenses of your opponents. Slow firing, high caliber weapons like Sniper Rifles and Pistols chew through Armor, but are weak against Biotic Barriers and Shields. Rapid fire weapons with a lot of projectiles, by contrast, like SMG's and Shotguns chew up Shields and Barriers quickly, but have trouble with armor. Assault Rufles are a bit of an odd duck as they're 'pretty good' at handling everything.
Additionally there are mods availiable for several weapon types that alter their capabilities. You can add Armor-penetration to an SMG or a shotgun, or a melee upgrade to a pistol or shotgun. Maybe a scope on your SMG to improve its mid-long range performance?
Finally, you may want to pair some weapons up with certain specialty ammo. For instance, SMG's are devestating in combination with Cryo or Incendiary Ammo as their high rate of fire gives them more opportunities to proc the special effects provided by these ammo types than, say, a slow firing shotgun.
Best Answer
You can find statistics for most snipers here: http://masseffect.wikia.com/wiki/Sniper_Rifles#Mass_Effect_3
The damage of Mantis and Widow is clearly different. Wiki data is often more reliable than the in-game charts.