The Wave Serpent is the Eldar's dedicated troop transport, an anti-grav skimmer that flies through the battlefield, blasting away with a twin-linked turret weapon while rushing to get your troops right into the heart of the army.
Like most Eldar vehicles, there is not much difference between it and, say, the Falcon or the Fire Prism besides some variation in weapons and armor. This is basically because the Eldar are shameless corner cutters who won't fix what ain't broken (though to be fair, the Imperium and T'au are also guilty in this regard). That or Games Workshop can't be bothered to produce multiple different molds and prefers to use the same one as the staple Eldar one.
On The Tabletop
Thanks to the 6th Edition Eldar Codex, the Wave Serpent was regarded as a massive chunk of cheese on the tabletop thanks to three factors: a massive amount of accurate, long-ranged mid-strength shots, high durability, and extremely spammable.
- How much firepower? The basic Wave Serpent has a twin-linked shuriken catapult, a twin-linked shuriken cannon, and the Serpent Shield, which wouldn't be so bad if it couldn't upgrade the twin-linked shuriken catapult to a shuriken cannon and the twin-linked shuriken cannon to a twin-linked scatter laser. What'll happen is it fires the scatter laser, it hits, and now the shuriken cannon and serpent shield are both twin-linked, meaning in total you are now firing four twin-linked S6 AP6 shots, followed by three twin-linked S6 AP5 shots (where 6's wound automatically and are AP2) followed by D6+1 twin-linked S7 shots that ignore cover and are pinning (the Serpent Shield itself also has 60" range). Now while the AP values of the shots are nothing special, regular GEQ's will still be ID'd by every weapon (and the Shield ignores the walls they're hiding behind), TEQ's will still be wounded on 2's and will take so many wounds you can count on them failing armour saves, so only MEQ's can afford to ignore it.
- How hard are they to kill? For starters, the Wave Serpent's front and side armours are AV12, which doesn't look that good until you see the Serpent Shield; every penetrating hit gets downgraded to a glancing hit on a 2+ (provided it hasn't fired its shield yet). Those lascannons you brought along? They're not going to do anything except chip off one or two hull points IF they get past the 4+ Jink save (or 3+ if you bought holo-fields for it).
- How spammable are they? Everyone on foot excluding Harlequins and Rangers may take them as a Dedicated Transport. They cost 115 points base and with the above gun upgrades cost 130 points. Seeing as how they are the Eldar's ONLY dedicated transport, and seeing as how there's no reason to not take Dedicated Transports you'll typically be facing 3-6 of them on the field.
The 7th Edition Eldar Craftworlds Codex moderately toned down the Wave Serpent. They still are strong bastions of firepower, but their abilities are less OP as fuck as they are decently strong.
- How much firepower? Still has the classic twin-linked shuriken catapult, shuriken cannon, but the scatter laser no longer gives laser-lock, and the Serpent Shield's rape-tastic shooting is now a once per game S6 Ignores Cover, Heavy 2D6. Result? Now have slightly less dakka than before, but are still spammable and can put out quite a few shots if you get lucky with the Serpent Shield.
- How hard are they to kill? With front and side AV12, fairly moderate AV Skimmer with the ability to jink and the infamous Serpent Shield intact. But, now if you dissipate the shield to shoot it once per game, you lose the benefits. In short, quite hardy unless you force them to shoot the shield/hit them with Ignores Cover weaponry. In addition, per the latest ITC FAQ, the Serpent shield is indeed a weapon, that can be removed by Weapon Destroyed. Sure it's unlikely, given the damn thing can negate weapon destroyed on a 2+, but I fucking dare you to roll a 1.
- How spammable are they? To make up for the lack of laserlock and the new Serpent Shield, it's now slightly cheaper and can still be taken by anything on foot. Still facing 3-6 of them in a list.