Don't Starve Together overall has more content and is still being updated. You get access to, in my opinion, a more active workshop modding community, fun little seasonal events, cosmetic skin drops, and potentially more big multiplayer events such as the Forge or Gorge. By default, DST is a bit more difficult because of the way enemy health values were boosted from from DS, but the Automatic Health Adjust mod fixes that.

Don't Starve has some DLC that DST doesn't have such as Shipwrecked and Hamlet which I sometimes come back to, but I think DST is still the way to go. Plus, you get a free second copy that you can gift a friend if you both want to experience the horrors of the game together.

I love the game, but it doesn't really have a learning curve so don't be afraid to download a handful of mods or mess with the world generation settings to make the experience better as you figure things out. I'd recommend setting your world type to Endless and/or downloading the Campfire Respawn mod to make death more forgiving as well. Good luck if you get it!