That is a very big question and the answer is largely dependent on the ship you're looking at, you'll get different answers for each. Some ships are much better suited to passive tanking than others, thats mostly down to the shield recharge time.
The idea of a passive tank is that every shield has a natural recharge time, this is a constant no matter how large your shield is. This in turn means the larger your shield the more is regenerated every second. For example if you had 100 shields which regens in 10 seconds it would be regenerating 10 shield/sec. You then add a shield extender and double your shields to 200, it will still recharge in 10 secs so will be regening 20 shield/sec. Passive tanks are purely the domain of shield tankers, armour has no natural regen and relies on repairers.
You build your passive tank with rigs and modules in 3 ways,
1) increase the shields size with shield extenders and extender rigs
2) decrease the regen time with shield power relays, power diagnostics and purge rigs
3) add shield resistance modules to reduce damage taken
All that is very simplified, the regen rate is not linear. If you were to graph it it would look like a bell curve with the optimal regen point around 33% shields. This means if youre taking damage and your shields drop below that point it's time to start warping as the amount of damage you can take is falling from that point on.
One of the biggest disadvantages of a passive tank is that it needs far more slots to build an effective tank than an active tank. The drake can field an awesome passive tank but to do so it really needs you to use most of the mids, most of the lows and the rig slots. This doesn't leave you a lot of room for damage mods or tackling.
In an ideal world your passive tank won't use any cap which means you're invulnerable to energy warfare. In practice there's a good chance you'll end up using active hardners.
Active tanking means you have a repairer or booster which you activate when you want to regenerate armour / shields, stating the obvious but worth saying
At its most basic you exchange cap for hitpoints. The capacitor operates on exactly the same principles as the shields, it regenerates in a non linear way and has an optimal recharge point around 33% or so.
Therefore active tanks are based around keeping as much capacitor available for as long as possible. This can be done in two ways
1) Increasing the regen rate so that it exceeds the rate at which you use it. Modules to achieve this would be
Capacitor rechargers, power diagnostics and rigs such as capacitor control circuits
2) Using charges which add capacitor when you are running low. Modules to achieve this would be Capacitor Boosters
Obviously option 1 uses far more modules than oiption 2. So in general, this is just my opinion and there are bound to be people who disagree or have exceptions Ada's Rokh for example, option 1 is best suited to PVE and option 2 for PVP. I have a few reasons for thinking this:
in PVE you are likely to have infinitely more time taking damage than in PVP so infinite cap means you can stay in a mission all day, if you use boosters youre time is limited to the amount of boosters you can store in your hold and they do take up a lot of space.
In PVP you will have short intense bouts of cap usage and you can keep adding cap as quickly as your cycle time on you cap boosters, you are limited to the amount you can carry though.
PVP requires a wider variety of modules to be really effective or excel so the fewer slots you need to use on your tank the better off you will be.
As far as skills go I'm not sure which needs more or less to be honest. I just have one last thing to say and that is DONT try and mix the type of tanking that you do on a ship. Pick a style that suits you and your ship and run with it. If you try to do a mix of active / passive you'll just end up having a ship thats crap at both.
ok, correction and flame retardant suit on, fire away