Ships & Modules

Your wording is a little unclear, are you asking about whether you should use a Manticore or a Widow to defend a mining op? Not sure what you mean by a black ops version of a bomber, because there is no black ops bomber there are bombers and black ops and these are wildly different ships with among other things a very large gap in the skills required to use them. Also what kind of space are we talking about here, high sec, low, null or WH?

If I assume non high-sec:

A solo Manticore will die almost straight away to anything that can reach it, like most frigate hulls it isn't very thick and is most likely to simply add another loss to your about to be wiped out mining op. Torpedoes apply poor damage to most targets and so your paper dps will be mostly imaginary in any practical situation, you need to be fighting battlecruisers or battleships to really land a good portion of that damage.

A solo Widow might be a nasty surprise when you decloak it but with poor lock time and decloaking targeting delay could mean a lot of things escape you if they just panic warp before you lock but ECM has real potential to save you from small scale gangs. That being said once they know you're there they will bring more to try and kill that Widow as it is a shiny mail to get, Third only to Supers and capitals in terms of desirability.

If we are talking high sec:

Solo Manticore will be able to get on some kill mails before CONCORD blaps the whole fleet but it's very unlikely you will kill any gank ships before they drop their target.

A solo Widow on the other hand has a real chance of jamming the aggressors if you are either not cloaked or decloak early enough to not have to worry about the targeting delay that it may be possible to save your barges assuming they have at least some tank on them. Just be absolutely sure you are only trying to jam ships that have taken criminal flagging, a Widow is a very expensive ship to lose to CONCORD. Although sitting there uncloaked there is a real possibility that the suicide fleet will simply go for your Widow instead of your barge and it will probably work. If you sit cloaked most ganks are done in the time it would take for you to decloak, wait 5 seconds, lock and jam.

EDIT: The Crow will not save anything ever, it's there to be immune to bubbles and tackle other ships to have your friends come in to destroy them. The Crow is very good at what it does but it will simply not do the job you are asking of it. Crows have neither the dps nor the e-war ability to get it done.

If you're in low keep the Widow cloaked and some distance off the miners so it can jam and escape. You might also want to use Procurors or Skiffs as they can get very strong tanks and some decent dps and so can hold their own against some of the more common combat ships in low sec and the Widow can jam what you can't fight to allow you to escape. That being said once you have decloaked the Widow it's time to move on.

If you stay where you are after showing your trump card people WILL come back to kill that Widow. You may even prompt people to add you to their contact watchlist and run locators on you when you log in if you get known for doing that. You'd probably be better advised to use a cloaked Scorpion than a Widow if you're committed to low/null mining as at least it won't hurt so much when it dies. Black ops are typically used in packs where they are dropped onto small gangs to blast them apart before disappearing with cloak to recover their capacitor to jump and/or portal back out of dangerous space.

If you're going to mine in low or null situational awareness is a much better defense than anything else and simply not being there when people warp in on you is your best option. This is not high sec so people will bring ships that are considerably better than a T1 destroyer because they have no intention of committing suicide here. You'll be able to fight off small numbers of small ships but it will ramp up fast if you do drive some off. People love seeing targets that look ripe for the picking.

Falcon is a more efficient and cheaper option to a widow to jam stuff out. your best defence is like people have said to just warp to a safe pos the second neuts enter your system.

I used to hang out with some random multiboxer dude which hade a pvp fit drake inside his orca.. when gankers stormed his mining fleet he switched one of the pilots into the drake and ganked the gankers.

A mining fleet is already capable of protecting itself. A fleet of skiffs with an orca can all refit to DDAs and RR off of an orca. Assuming you have 10 skiffs that is 3.5k dps from hammerheads. Without links they have 85k ehp and tank 197 dps per skiff repping it totaling a 1.8k tank. This will dunk on any t1 gang that doesn't have at least 4 logi. Spread ewar around the fleet. Some skiffs should have long point, others scram, and others web. The great thing about skiffs is that they have massive buffer and high scan res so they are super forgiving in an rr gang.

Have your gang members practice refitting quickly when spooky men enter local, how to follow rep broadcasts, how to follow primaries etc and make massive plays.

[Skiff, Elite pvp]
Damage Control II
Drone Damage Amplifier II
Drone Damage Amplifier II

Warp Disruptor II
Small Capacitor Booster II, Navy Cap Booster 200
Adaptive Invulnerability Field II
Thermic Dissipation Field II
EM Ward Field II

Medium Remote Shield Booster II

Medium Anti-Kinetic Screen Reinforcer II
Medium Core Defense Field Extender I

Hammerhead II x5
Warrior II x5
Acolyte II x5
Navy Cap Booster 200 x58

Weather or not they have a targeting delay, is irrelevant, it's a battleship, so it has a Shite scan resolution.
it will always lose from a falcon who is able to use a Covert ops cloak as well.

and the Stealth bomber is the only one that has 0 targeting delay after declaoking.

as for protection o your mining operations. if you want to stay cloaked use a T3, Protheus is an excellent shark.