All this data is potentially out of date, and should be taken with a truckload of salt
Player Notes... Since the inception of Rubicon patch, and probably earlier, the advice given in the following article is outdated. Weapon slots have since been changed in favour of Missile Launchers, bringing the Cyclone further into its more intended purpose of laying down additional firepower in Fleet Operations, and therefore somewhat less viable in solo combat. This is further evidenced by its ability to fit Warfare Links, a trait shared by the other three "Tier 1 Command Ships".
File:Azual skoll icon.png Know Your Enemy by Azual Skoll, The Altruist
The cyclone is unusual for a tier 1 battlecruiser in that relatively little separates it from its tier 2 cousin - the brutix and ferox are split from their counterparts by weapon system, while the prophecy and harbinger are differentiated by being tank and gank respectively. The cyclone and hurricane however, don't have all that much that splits them apart - both are turret (and most commonly autocannon) ships, and both are commonly shield tanked (probably not the intention when the hurricane was designed, but it's the way things have turned out). Where there is a difference (such as with the ship's turret layouts), it usually favours the hurricane. There's really just one thing that the cyclone does far better than the hurricane - I mention this not to demean the ship, but because when someone chooses to fly a cyclone they very often do it because of this attribute. That thing is active shield tanking.
With 5 mids and a 7.5% per level bonus to shield boost amount, the cyclone can mount a strong active tank. We're not talking myrmidon levels here (more like the brutix), however as a shield tanker it can do this without compromising its speed or damage output. While it can't tank enough to be significant against an opposing gang (excepting small frig gangs and the like), it's strong enough to turn the tide in a 1v1 engagement (in fact active tanked cyclones often beat their big brother the hurricane in such a scenario). The cyclone can also mount a fairly beefy shield buffer, which is an equally viable option, although this is less common on account of the hurricane's effectiveness in that role.
Offensively, the cyclone suffers from a partially split weapon system. It only gets 5 turret hardpoints and a single damage bonus, while the remainder of its dps is provided by up to three launchers, and 40m3 of drone bay/bandwidth. Combined these actually offer roughly similar dps to the hurricane, however getting maximum effectiveness out of all three weapon systems together is both player skill and character skill intensive. Additionally, the cyclone (assuming it fits launchers to provide comparable dps) lacks both the free high slots of the hurricane and it's additional low slots for tracking enhancers and speed mods.
If this writeup has given you the impression that the cyclone is a poor ship, I should probably clarify that it isn't - it's very capable especially when your character skills are well developed. It's main problem is existing in the shadow of such a popular ship as the hurricane, and it's difficult to talk about the cyclone without drawing comparisons. As with underdog of course, there's always the advantage of being constantly underestimated by your opponent - a valuable trait for solo PVP.
Fighting a cyclone can be tough - most will try to kite, taking advantage of their long falloff range and also reducing they amount of dps they are forced to tank. The cyclone has a similar base speed to the hurricane, although with fewer low slots it tends to be slightly slower than a shield cane in practice. While many cyclones will fill their spare high slots with launchers, neuts are still fairly common and should be expected. The biggest disadvantage of the (active tanked) cyclone is probably its lack of mid slots - it has just enough to make it work, but it still feels the pinch; cyclones will very rarely fit webs or any additional ewar other than a point or scram, leaving them with three slots - one for a cap booster, and two for a shield booster and a hardener. The result is a tank which while fairly strong, but can break quite easily under cap pressure leaving relatively little EHP behind. Especially if the cyclone is running a neut, cap warfare, a drawn out fight, or simply bad piloting can quite easily break it. You're usually best fighting close and maximising your own dps, since mitigating the damage it receives (and thus taking pressure off their active tank) is exactly what they cyclone pilot wants. Since active tanks more often use shield boost or cap rigs rather than resist rigs, EM is generally the best damage type to use against the cyclone, with thermal second.
Below are additional ships images. Click the image below for a larger version: