What can you do in minecraft that you can't in Terraria, with the exception of a third dimension, which, in my opinion, you don't need?
/runonandonandonandonsentance
The 3rd dimension adds a whole lot to immersion and environment.
There's some Minecraft mods, for example, that add echo effects and ambient biome sounds. They're small mods, mostly, but the feel they give is just amazing.
I tried to imagine how much of a difference it would make in Terraria and found that it wouldn't be as good, just due to a lack of a third dimension, and thus, immersion. Have you ever been amazed when you broke open a rock and found some mineral behind it? No, because you can already see things behind rocks. Have you ever been startled by a monster coming up right behind you? No, because of the 2-D camera view.
Infinite worlds. You can keep on exploring for as long as you (and your computer) can take it, instead of "huge" (pffffft) worlds that you can walk across in five minutes.
Randomness. You always know where stuff is in Terraria. "Oh, there's a jungle and dungeon to the left or right, corruption about 1 minute from spawn on either side, ocean on both sides, and hell below." In Minecraft, the seed system is the only thing that will guarantee for something to be in the same place twice.
Easy enemies. Although there are enemies that are a good deal tougher than anything Minecraft has seen (namely hornets, once they got their shooting stingers) there's still lots of knockback involved, and the lack of a third dimension means things can't really surround you unless you jump into them first, and things can't sneak up on you like creepers can. Not to mention, for Minecraft there's mods making enemies smarter: not so for Terraria. In fact, this brings me to another topic:
Mods. After playing any vanilla game for oh so long, and waiting for the next update like a crack addict, it becomes necessary to install some mods. Long story short: Minecraft has tons, Terraria has none.
Environment. Although Minecraft's biomes are lacking in many areas (You call THAT a swamp?!) It has much more variety in the environment. In Terraria, you get the same old trees... same old grass... same old rabbits for miles around.
Community. While Minecraft's community is split in many ways over their opinions of updates ("Oh, great! NPC Villages, how cool!" "AUGHH NOO I DON'T WANT loving NPCS") it's much more interesting to talk about updates with them, than with Terraria's mostly single-minded community.
For every update, I read the posts and "Oh, cool! Amazing! cn't wait <3 lol so awesome" Occasionally there's someone who points out a valid flaw in an oncoming feature, and then he promptly is torn apart by the other users like

s.