Does Skyrim: Legendary Edition have anything except the old DLC?

No. It is simply a compilation pack.

The additional difficulty level and removal of level cap were added to vanilla Skyrim in a patch (patch 1.9), according to the Elder Scrolls Wiki (which links to the official blog as a source)

Additional quote from the Bethesda Blog:

Coming to Xbox 360, PlayStation 3, and PC on June 4th for $59.99 (European territories will see its release on June 7th), this package includes the most up-to-date version of the original game (employing the 1.9 title update),as well as the game’s three add-ons: Dawnguard, Hearthfire, and Dragonborn.

Info from the Bethesda Blog about update 1.9 (note that it states PS3 and Xbox, but the patch was released for PC before the consoles. The console one is unchanged except for specific bug fixes):

NEW FEATURES

Legendary difficulty setting

Legendary Skills – Skills of 100 can be made Legendary. This will reset the skill to 15, return its Perks and allow the skill to affect leveling again. This effectively removes the overall level cap.