The combat system has been redesigned and simplified. The original "wheel" has been replaced by a layered tree; even though it is still called wheel.
Weapons have power "pips" now in addition to the quality level colours.
The crafting system has been changed completely; instead of collecting, refining, and using materials the weapons consist of, you now "add" surplus weapons to the ones whose power you want to increase.
One of the appeals of The Secret World is that it has no Classes or Levels - which makes your Character more individual. But this was too challenging for many new players; so Secret World Legends now has the familiar predefined classes, and levels. The classes are, though, only a guide for starters; you can later spend your AP and SP points freely to achieve the "mix" TSW sports from the start.
The first game areas have been "railroaded", the quests therein been simplified. Also, mission areas are sometimes warded by a wall of hexagons to show you the boundaries; and trails have been marked with shining hexagons too.
This serves the purpose of helping new players; other players have commented this breaks immersion and suspense / thrill for them.
The changes to the core game hub Agartha, though, are generally regarded as improvements - orientation is easier and travel faster.
Secret World Legends follows the current F2P business model: there is an in-game "gold" currency you can buy for RL money, which allows you to buy vanity items and timesavers. TSW, for comparison, has a base price, and new content "issues" (beyond the large volume of base content) cost extra.
There are more in-game currencies now. Trading between your own characters is impossible as of now, so no "mules".