The Crystal Tower is very similar, but it does have some significant differences to its appearance and story in III. So, here's a Cliff's Notes version...
In III, it's just kind of there as Xande's stronghold. In III, Xande was one of the Archmagus Noah's apprentices along with Doga and Unei. When he reached the end of his life, Noah gifted his apprentices each with their own special power: Doga was given power over magic, Unei was given power over dreams, and Xande was given mortality.
Naturally, Xande wasn't very happy about that, and began scheming a way to grant himself immortality. To this end he flooded the world in a dark ocean, stopping time everywhere but on a floating continent, and holed himself up in the Crystal (Syrcus) Tower. He remains there until confronted by the party, attacking them through proxies in an attempt to stop the Warriors of Light from gaining power from the Crystals necessary to defeat him. Xande has no pact with the Cloud of Darkness in III, but his actions inadvertently end up summoning it after his death at the hands of the Warriors of Light.
That's significantly different to XIV's incarnation - notably III Xande has the exact opposite goal of XIV Xande. All the bosses are taken from III monsters, and there are a ton of references, but the Crystal Tower series isn't a carbon copy of III.
Shadow of Mhach is mostly original. Mostly. Some of the bosses are references (Cu Chulainn, Echidna, Ozma, Calofisteri, Diabolos) and the War of the Magi is used as a backdrop, but it expands the lore of XIV greatly without relying too much on previous titles and delves much further into the Celtic Ulster cycle mythos in so doing.
Return to Ivalice... is a lot like III in the sense that it takes elements from previous title(s) and rearranges them to fit XIV's world, but it feels like locations from Ivalice titles were just grafted on rather than adapted (or Hydaelyn was adapted to fit the Ivalice elements, when it should be the other way around). Leaving aside my personal distaste for Ivalice, that's my biggest gripe with it.