Ships & Modules

If you're flying Amarr, then definitely go with armour.
If you're flying Minmatar, then train both.
If you're flying Gallente, train armour and a bit of shields
If you're flying Caldari, train shields.

Shields have the advantage of an XL booster, while armour gets the XL plate.
Shields have the disadvantage of increasing sig radius, while armour ships lose speed.
Shield boosters are inefficient, yet powerful and start at a cycle's beginning. Armour reps are very efficient, yet don't have the pure burst capability of shield boosters.
Shields have lower base resists, but invulnerability fields are more powerful than EANMs.
Shield ships can devote lows to speed and weapon enhancement modules, while armour ships can devote mids to ewar.

First off, train both. Getting an effective T2 shield tank takes something around 14 days of total training time. Armor takes a bit longer, but that's because you want the armor comps at 4.

The paper advantage of a shield tank is more DPS than armor, since it frees up lowslots for damage and projection mods. The paper advantage of armor is superior buffer, leading to more EHP. Obviously this is not true across the board and the exceptions are very numerous.

You said beam and pulse so I assume you're speaking about Amarr.

Amarr are the armor tanking faction. They receive armor resist bonus on some hulls, all logistics have bonus on remote armor rep, they have much more low slots than med slots. So you're better with armor tanking most of the time. Escpecially since amarr offers a really good damage projection which is necessary because armor tanking slows your ship down.

On the other side: with that many low slots + good damage projection + good base cap on most Amarr hulls they are quite good when nano fitted. Which means a slight shield buffer in med slots and alot of damage + tracking/range + speed mods in low slots. Amarr have quite a good base speed but a rather bad agility. This will be adressed by fitting agility mods in the lows. Amarr have plenty of them.

Downside of Amarr nano fittings is they are not really failsafe. Pulse laser have the worst tracking of all short range turrets. They are vulnerable to almost all forms of ewar. On top the shield buffer isn't really huge because of only few med slots. So if all works as planned Amarr nano shield fits are deadly, of something goes wrong you're dead quite fast.

Shields naturally regenerate with time, armor can pack on more "raw" HP.
Shields free up the low-slots allowing for more weapon-enhancement mods, armor frees up medium-slots allowing for more "utility" and Ewar mods.
Armor is generally "easier" on your ships' capacitor, shields can create incredible active tanks.
Armor slows a ship down, shields make a ship appear "bigger" to sensors and weapons.

However cap rechargers with no drawbacks apart from taking up a slot fit in the mids so you can use those unused slots for cap stability. However armortanks cripple DPS as the lowslots are used for the tank. As shield has to use mids for the tank they cannot use any capacitor mod without drawback, they have only rigs.

One thing to be noted about shields tho is passive tanking, you may look at a passive PVE fit and see "oh only 300 recharge rate? that's not good enough!". Well don't be fooled, its coefficient recharge curve, at around 33% shield the shield hits its peak recharge rate which multiplies it with 2.5

So your tank recharges 750 shield per second instead. However at around 20% it drops like a rock, yes your tank become weaker after the peak. So if you passive tank and warp out at 50% cause omg it isn't recharging! Do know at around 50% the coefficient curve starts, that's where the passive tank starts to shine If you go below 20% however, well, time to get out.

Active armor tanking can PVE but cripples DPS
Active shield tanking can PVE and deals maximum DPS, however in most cases not capstable, needs micromanagement
Passive armor tanking Cannot PVE
Passive shield tanking do work quite good for PVE but you cannot really use damage related rigs.

On another note smaller shield boosters have shorter cycles, armor repair modules all have long cycles in comparison. As an example Two small DED shield boosters can equal a DED large armor repairer in effectiveness with some shield boost amplifier, and they use virtually no capacitor in comparison. Now that varies from ship to ship how effective using smaller reps are. Armor can never make use of smaller reps, only more fancy ones with more repaired per cycle.

Now i have the luxury of alts, i have a vulture boosting my tengus, so when my main joins in on the fun i want her to shield tank as-well but Ah she flys a vindicator, hmm, what to do. Something that armor cannot do even with bonuses of CMDships and pirate implants. She has a Crystal set and this Vindicator fitted which is the first time i share it with anyone, cause people will cry if they see it. And with the luxury of tengus taking care of frigs. With the two 5% damage related hardwirings, i present to you probably EVEs most derp vindicator in existence. Defying laws of tanking thanks to OP shields, this is why shield tanking is way better than armor.

The 1341 DPS Vindicator with 999 DPS omnitank (12 minutes), more than enough to finish missions. (not running active shielding II ganglink, with it 1424 DPS omni tank for 7 minutes and 5 seconds)

[Vindicator, derp]
Federation Navy Magnetic Field Stabilizer
Federation Navy Magnetic Field Stabilizer
Federation Navy Magnetic Field Stabilizer
Federation Navy Magnetic Field Stabilizer
Republic Fleet Tracking Enhancer
Republic Fleet Tracking Enhancer
Republic Fleet Tracking Enhancer

Pith X-Type Shield Boost Amplifier
Pithum A-Type Medium Shield Booster
Pithum A-Type Invulnerability Field
Pithum A-Type Invulnerability Field
Federation Navy Tracking Computer, Tracking Speed

425mm Railgun II, Caldari Navy Antimatter Charge L (from LP store cheap)
425mm Railgun II, Caldari Navy Antimatter Charge L
425mm Railgun II, Caldari Navy Antimatter Charge L
425mm Railgun II, Caldari Navy Antimatter Charge L
425mm Railgun II, Caldari Navy Antimatter Charge L
425mm Railgun II, Caldari Navy Antimatter Charge L
425mm Railgun II, Caldari Navy Antimatter Charge L
425mm Railgun II, Caldari Navy Antimatter Charge L

Large Capacitor Control Circuit II
Large Capacitor Control Circuit I
Large Capacitor Control Circuit I

Garde II x5

That would be great, except that armor doesn't regenerate. It buffer tanks, fine, yes, everyone agrees on that. But there is no such thing as a passive armor tank because there's no way to get armor back without cap use.

If i hadnt lost interest in EVE as of lately maybe, and all they would see are my passive tanked tengus, they can try to gank them all they want but they would need more isk in shooters than if all the tengus mods dropped :).

Just pointing out that when it comes to PVE, even armor tank battleships with armor tank bonuses work better shield tanked, with the proper support for it obviously, but still. Armor does not have that support, it lacks so much when it comes to PVE. Forgot to mention i do not run the active shielding ganglink tho, 1434 DPS omni tank with it on, but only 7 minutes and 5 seconds with it. Only use it for short missions with tons of incoming DPS such as whats it called, mercs, stop, theif, stop the thief? Also for snipe mishs instead of tracking comp a sensor booster.

Shields > armor

If you take armor damage as a shield tanker you are doing it wrong.

Absolutely right. I was meaning the mods available for resists, without cap usage. My bad, on terminology.