The Falcon is, in fluff at least, the Eldar main battle tank and the most common vehicle on the battlefield. It certainly was in previous editions, when a Falcon with holofields was absurdly difficult to kill. Unfortunately, the Falcon has lost its place in this edition.
The Falcon has the standard Eldar grav-tank chassis and armor, and comes armed with a pulse laser (essentially a 2 shot bright lance without the Lance rule), a shuriken cannon, and twin-linked shuriken catapults. The cannon can be upgraded to any of the standard Eldar heavy weapons, and the catapults can be upgraded to a shuriken cannon. The Falcon can carry 6 passengers, so it can act as a transport for a small squad.
The problem with the Falcon is honestly the Wave Serpent. The Wave Serpent is more durable due to its shields, can carry a larger squad, and packs better firepower. The serpent shield is a much better gun than the pulse laser against anything but a 2+ save target, and the Serpent’s secondary gun is twin-linked, while the Falcon’s is not. Not only that, but the Serpent is a bit cheaper than a comparatively armed Falcon and doesn’t take up a Heavy Support slot. The Falcon is just out-classed.
The Fire Prism is the Eldar’s heavy firepower tank, but it has the same mobility and armor as all Eldar tanks. Its claim to fame is its excellent prism cannon, which can fire in three modes. In dispersed mode, it’s a S5 AP3 large blast, excellent for taking out large units of infantry, particularly Space Marines. In focused mode, it becomes S7 AP2 blast. I find this mode least useful, really only being the most efficient against squads of Terminators. Finally, it can fire as a S9 AP1 Lance, which is amazing for taking out vehicles and monstrous creatures.
The Fire Prism is a great tank. While it’s only as durable as any other Eldar tank, it has very flexible firepower and will deal with just about any target it needs to. Also, it’s fairly cheap for such flexible firepower. Its main downfall is that it’s all combined into one gun. If it suffers a Weapon Destroyed damage result, it can lose almost all of its usefulness. Even so, it’s a great unit.
The Night Spinner is the newest addition to the Eldar grav-tank line-up, and is once again built on the same chassis as the other Eldar tanks. It carries what is essentially a larger version of the shadow weaver, called the Doomweaver. The Doomweaver has a couple advantages over its smaller predecessor. It’s a barrage large blast, and it’s S7; this last bit is huge since it means that it’s S8 against vehicles. This makes it great at damaging tightly packed vehicles as well as just about any infantry in the game.
It doesn’t end there. If the enemy gets close, it can fire as a torrent weapon. This allows it to do tons of hits on anything that gets close to it, and is particularly useful against light infantry (of the sort that tends to outflank and get close to you artillery pieces).
The Night Spinner is a really useful tank, and fills a unique niche in the Eldar army. It provides hidden long range firepower that can threaten both tanks and infantry. Don’t forget to target important enemy characters; the Doomweaver can cause so many high strength, pseudo-rending hits on the model at the center of its blast that it will have to be very lucky to survive.