What does Hyrule Warriors Legends have that Hyrule Warriors doesn't?

(This list may not be complete as I haven't unlocked everything in Hyrule Warriors Legends yet.)

Most of the game is pretty much identical to the original Hyrule Warriors for Wii U, including that game's DLCs. It does however add quite a bit of new Content. Other than that, some gameplay aspects and battle rewards have changed. Also note that Challenge Mode is missing from the 3DS version, as well as the ability to play with another person.

Additions

Playable Characters: There are five new playable Characters in Hyrule Warriors Legends: Linkle, Skull Kid, Toon Link, Tetra and King Daphnes. All these characters can also be unlocked in the Wii U Version using a download code provided with the 3DS version. This makes them not technically exclusive to Legends, but I included them anyway since you do need to own both versions to play them on the Wii U.

Legend Mode Chapters: There are at least two new campaigns in Legend Mode, each of which consist of multiple Battles. The first campaign is unlocked gradually as you play through regular Legend Mode, the second one can only be accessed after the main story line is completed (including Cia's chapters that were added in the Wii U's DLC). Both these campaigns focus on the newly introduced characters, and they feature at least one new map and boss.

My Fairy Mode: Throughout Adventure Mode, you can now collect fairy companions, food and accessories. The fairies can be leveled up by giving them food, and their stats improve if you give them accessories. You can then pick one of your fairies every time you start a battle (in any mode) so they can help with various skills and their own type of magic.

Items: In addition to the items from the Wii U version (bombs, boomerang etc.), Hyrule Warriors Legends adds a Hammer and an Ocarina. The Hammer is similar to the other attack items, while the ocarina enables you to quickly travel between owl statues scattered around the map (the statues are battle-specific; on the same map, they can be in different locations in different battles, or they can not be there at all).

Adventure Mode Map: The 3DS version also features a whole new map for adventure mode with its own rules and item cards. It is unlocked by completing the regular adventure map.

Changes

Rewards: While the battles in Adventure Mode appear to be mostly the same as they were in the Wii U Version, many of them have different rewards and treasures, specifically items for My Fairy mode. Some adventure modes also have changed enemy characters and allow you to unlock the characters that were previously introduced as DLC on the Wii U version. Some Legend Mode rewards have changed as well (for example, Cia's chapters now actually have heart pieces and skulltullas in them).

Team fights: While the two player option from the Wii U has been removed, the 3DS version lets you control multiple characters in most battles. You can switch between your characters at any time (sometimes acces to them needs to be unlocked by completing a certain mission, though this seems to be exclusive to Legend mode). While you're not controlling a character, you can send them to specific locations on the map or give them tasks (capture that keep, attack that enemy etc.). If you gather your playable characters around a boss, you can unlock bonusses, which are similar to the ones you get from using magic.

Some minor changes also include new side missions in certain battles.

Be aware that more content will be added to the 3DS version via DLC, and only parts of it can be unlocked on the Wii U (if you own both versions). There may also be a small chance that some or all of this could be released on the Wii U version at a later date, but that is pure speculation on my part.