When you try playing Don’t Starve Together for the first time, the game recommends you to play Alone mode.
Does Don’t Starve Together – Alone mode make the original Don’t Starve obsolete, or does the original Don’t Starve have unique content in it’s own right compared to Don’t Starve Together – Alone mode?
The two versions of the game are balanced differently in terms of difficulty.
As you can read in this discussion on the Steam Community, one of the devs says exactly that: you can play Don’t Starve Together as a solo game, to start to grasp the mechanics, but as you start to progress you’ll find harder content than the “base” version. Some of the challenges that Together makes you face are not meant to be tackled by yourself. Take for example the Ewecus: its spit can trap you for a few seconds and, while it could be overcome by having a friendly Pigman, having another player come to your aid makes the fight significantly easier.
In addition, at the moment of this writing, Together features the content of the base game and Reign of Giants, but not the Shipwrecked content.
Many things were modified or rebalanced too, due to the intrinsic power of some of the characters, and special encounters and events have been added to adapt to the multiplayer aspect. You can read the whole list of differences on the wiki page.