With the light dictors, you'll remember they launch bubbles like probes - diving in, dropping a bubble and then returning to safety (or attempting to do so) until they are needed to repeat the process. The heavy interdictor on the other hand deploys its bubble as an activated high slot module, with the effect centred around the ship - where the ship goes, the bubble follows. While the bubble is active, the HIC suffers a number of limiting effects - most notably it cannot warp, its MWD or AB speed boost is significantly curtailed, and it cannot receive remote repair from friendly logistics ships. This means that while the HIC is far more durable in of itself, in order to fill its role it much remain on the field, and must do so unsupported.
In practice this means that while light interdictors often operate as free agents - darting around the field to drop bubbles, scouting ahead or holding behind, the HIC is vulnerable filling it's main role anywhere other than under the massed guns of its own gang. The fact that the HIC has to remain in it's own bubble to keep it up makes it noticeably less flexible than its light counterpart - staple tactics such as dropping drag bubbles at range from your gang or placing stop bubbles behind yourselves as you flee aren't possible without sacrificing the HIC in the process. However the HIC does have its strengths; it is fairly common for an opposing gang, upon jumping into your camped bubble, to immediately primary your light dictor - it's a very soft target, and killing it removes your ability to drop additional bubbles and trap the opposing gang. The HIC makes a far tougher target, typically falling right to the end of the primary list and thus keeping your bubbling capability in tact throughout the fight. This combination of attributes means that while the light interdictor tends to fill a very flexible role as a bubble manipulation tool, the HIC's role is relatively simple - sit on the gate or gang, bubble up, and tank. Due to their relatively low damage output and poor manoeuvrability, HICs are usually (but not always) employed in gang, and are not common solo ships.
In general, the HIC is most effective in medium to large engagements with fairly static fleets (such as battleships), where the fast tackle capability of a light dictor is not required, and the hostile damage output is not yet up to the level that would make a HICs quite substantial buffer tank completely trivial. They're also particularly popular for tackling supercapitals (which as you may know, are immune to all targeted electronic warfare modules including conventional warp disruptors). However, I have to claim a certain amount of ignorance regarding this kind of warfare - while Agony has fought and killed supercaps in the past both as a corp (before the HP buff) and with the help of others, doing so falls outside my area of expertise and definitely outside the scope of this article.
HICs also have the option of loading a script into their warp disruption field generator which effectively turns it into an infinite strength long point. While this doesn't offer a significant benefit over a regular long point in most circumstances, it does allow the HIC to lock down stabbed haulers and deep space transports (which have an innate +2 warp core strength). This, combined with a strong enough tank to shrug off gate guns, makes the 'infinipoint' HIC the tool of choice for lowsec gatecamps.
The ships themselves are all fairly similar - they receive almost indentical bonuses, share each other's strengths and weaknesses, and are flown in pretty much the same way. Because of this my analysis of the individual ships will be relatively short, while my analysis of the class as a whole (which you've just read) will be more detailed than usual.
The radius of a HIC's bubble is 20km with HIC V (the same as the light dictor), while the range of its scripted module is 30km. These modules cannot be overheated to increase range like a conventional point, nor is their range affected by gang bonuses.
Onyx

A standard onyx features a four slot shield buffer tank, plus a MWD and one mid slot for utility purposes (often a sensor booster for when using a scripted point, or possibly a web to help keep targets inside its bubble). This will be supplemented by a rack of either HAMs or HMLs along with one or two warp disruption field generators (it's fairly common to have one for the bubble, and one scripted to hold individual targets since the scripted version has a longer range). Low slots are typically used for damage mods, however some fits will fit power diagnostics to take advantage of the shield HP increase and achieve as strong a tank as possible.
What separates the onyx from the other HICs is its range. With heavies, the onyx can hit out to its max targeting range of 110km (assuming leadership bonuses) without trouble, and potentially a little further if sensor boosted. Even with HAMs, it can manage a respectable 25-30km. Aside from that, it's relatively uninteresting - moderate tank, moderate speed and moderate dps.
Having no drones, and unlikely to be fitting neuts or any mid slot tackle (a web is possible as I mentioned, but a sensor booster seems to be more popular), the onyx is quite a vulnerable ship if caught alone - it can be held quite easily by a single frigate, and while its buffer tank is substantial it won't last forever. Due to its caldari racial resists, the onyx has quite a large EM resist hole in its tank. This will usually be patched in some form, but will still be either its lowest or occasionally its second lowest resist. Your next preference should be explosive, with kinetic and in particular thermal resists being very strong.
Broadsword

Typical fits are almost identical to the onyx fit mentioned above, with launchers exchanged for medium calibre autocannons (usually 220mms). The falloff bonus does make the broadsword quite versatile, and with its low slots for damage the broadsword typically has the best damage output of the four HICs, albeit with shorter effective range than the onyx and with an overall damage output still slightly lower than the rupture. While some people (more in lowsec as I understand it) do use broadswords as pseudo-dps ships, it isn't really anything to write home about.
Where the broadsword does shine is in its tank. It's rare for a minmatar ship to out-tank its caldari counterpart, but thanks to its minmatar racial resists the broadsword does just that! Where the onyx has to use slots to plug its large EM hole, the broadsword begins with balanced resists and goes from there. Typically you're looking at a slightly stronger tank than on the onyx, with kinetic resist lowest followed by explosive, thermal, and finally EM.
As with the onyx, the broadsword is fairly vulnerable up close due to its lack of anti-frigate defence, providing you can get under the tracking. The higher speed plus the better performance of autocannons against un-webbed targets makes the broadsword marginally more threatening than the onyx, however it remains far more dangerous as a gang tackler or bubbler than it does as a solo ship.
Phobos

The phobos is unusual in a couple of respects. Firstly, it had a resist bonus rather than an armour rep bonus - an oddity among gallente ships. Secondly, and somewhat ironically given the first point, it is the only HIC which is commonly active tanked. I attribute this to the easier job of fitting an effective active armour tank compared to an active shield one, while still having plenty of mid slots for tackle and cap boosting (which the devoter lacks).
There's less of a 'standard' fit for the phobos than there is with the shield HICs, and it's fairly common to see phoboses fit with single or dual 1600mm plates, dual reps, or a mixture of buffer and rep. A dual rep phobos can field a fairly substantial tank, although not quite to the same proportions as ships like the myrm. Similarly a heavily plated phobos offers an excellent buffer, generally similar to the broadsword in terms of EHP. Due to its reasonably good mid slot count, the phobos is the most likely HIC to be fitting one or more webs, making is probably the least vulnerable HIC if caught in a solo environment. That said, even with the bonus its blasters have a fairly short range, and due to relatively weak grid it can be difficult for the phobos to fit anything larger than medium electron blasters. Outside 10km, its damage is likely to be poor to non-existent. Some phobos pilots even opt to fit small guns or no guns at all, boosting their tank instead.
While blasters have excellent damage as a weapon system, the phobos' lack of drones plus the use of its low slots for tank gives it a fairly poor damage output compared to most equivalent gallente ships, and generally worse than the two shield HICs. While its mid slots provide defence against light tackle, this isn't all that dangerous a ship in of itself.
As a gallente t2 ship, the phobos receives fairly hefty bonuses to kinetic and thermal resists. Explosive is left as an obvious hole, but an explosive hardener is fairly easy to fit. Against most phoboses, you're likely to find explosive and EM resists roughly tied for the lowest position (gambling on eplosive in case there is no hardener is probably a reasonable call), followed by thermal and with a high kinetic resist.
Devoter

Devoters aren't usually active tanked due to their lower mid slot count, however some will feature a rep alongside their buffer tank. It's possible to fit two or even three 1600mm plates on the devoter, giving it the strongest buffer tank of the HIC line, at the cost of poor damage output (you can't fit three plates alongside medium guns, and even two can be a struggle) and making this already slow ship very sluggish.
While a web is possible the devoter falls into the same category as the shield HICs when it comes to vulnerability. While it's possible for the devoter to fit a neut in its spare high slot, most devoter pilots opt for a second warp disruption field generator or perhaps a gang assist module like a cyno.
With its robust tank, the devoter is the HIC of choice for large armour fleets which require plenty of buffer and little else, however with its low damage output it's probably the least threatening of the four in terms of the actual danger it presents outside of its bubbling capability. With strong amarr t2 resists the devoter naturally receives a fairly even resist profile, with thermal and EM falling lowest. However, it's fairly common for devoter pilots to plug these holes due to their copious low slots. Assuming an EM and thermal hardener (a fairly common choice), kinetic will be their lowest resist followed by thermal, EM and then explosive. Thermal is a decent gamble option since it's still the second lowest if filled, and the lowest if not.