With some notable exceptions, weapons categorized as "siege" tend to deliver low to middling damage across a broad area at a very short range. They also tend to consume huge amounts of weapon energy, which can compound their slow rate of fire by having to pause to recharge. There are no repeating (Gatling) siege weapons -- each is one shot at a time. A couple of them are "charged" weapons, meaning you have to hold the trigger for a second or two while it charges up, then release the trigger to fire.

Given those drawbacks, most siege weapons aren't something you'd probably use in normal combat. Where siege weapons really stand out is in being able to deliver the damage through heavy armor. As the Collections screen for siege weaponry notes, this is mainly of value against structures and bosses. I'll add that "bosses" includes demi-bosses, particularly including some very difficult foes that appear at the climax of one of the campaigns. I also suspect it includes armored outlaws.

You need to keep in mind, though, that when it comes time to use a siege weapon against a boss or demi-boss, you'll probably want to have leveled up your skills with it. So maybe use it -- or just have it mounted -- while engaged in combat that doesn't require a siege weapon.

Flamethrower: This is the one siege weapon that everyone has, because it comes in the starter kit. The Act I tutorial plays the Flamethrower up a bit. It's recommended against the imps due to its broader damage area, then against the cyclops as part of an elemental combo, then against the imp hive and extractor because you're attacking structures. But the Flamethrower exhibits all of the limitations previously mentioned for siege weapons.

Levitator: A homing missile with a long range, combined with Stasis effects that few foes are resistant to, makes the Levitator a very popular siege weapon. The long range translates into hitting only one target at a time, but since it's homing, you don't need to aim precisely. Energy drain is the highest of all weapons of any kind, and fire rate is slower than any other siege weapon.

Fury Cannon: This extra-cost weapon (retailer-exclusive Scramble toys package, or paid DLC) may be the siege weapon par excellence. Compared with Flamethrower, it delivers twice the damage at twice the range with 25% less energy drain. Field of fire is noticeably tighter due to the longer range, and refire rate is slightly slower. Unless you need a broad field of fire, the Fury Cannon leaves Flamethrower in the dust.

Tidal Wave: This extra-cost weapon (paid DLC) might look like it's just a Shockwave with Stasis/Lift effects added, but don't be fooled. The Tidal Wave is a siege weapon while Shockwave isn't. Unusual for siege weapons, Tidal Wave has twice the range and a considerably tighter beam than Shockwave. Other than that, TIdal Wave has the usual "siege weapon" disadvantages when compared with Shockwave: damage effects are a bit less, fire rate is slighly slower, and energy usage is much higher.

Gauss Gun: A rail gun with the distinctions of being the only "precise" siege weapon and the only "kinetic" siege weapon, the Gauss Gun is a charged weapon. It boasts the greatest range of any non-missile siege weapon. Compared with Fury Cannon, it delivers slightly less damage (and no Fire status effect) with the same energy usage and fire rate. The need to charge before each firing tends to reduce the effective fire rate, though. Being a precise weapon, the Gauss Gun can benefit from Expert Ammo and can deliver "critical hits.".

Imploder: A charged weapon that delivers performance similar to the Gauss Gun, but with Gravity/Vortex status effects rather than precision hits. Compared to the Gauss Gun, the Imploder's damage is slightly less (not counting the status effect), with the same range and rate of fire. Energy usage is a bit lower than Gauss Gun.

There are no siege weapons with Cold status effects.