To compare the two, Minecraft, due to being 3-D, is a game much more about the mining, the exploration and the crafting. It's more satisfying to wandering around a 3-D (if blocky) world and build these massive mega-structures.
But Minecraft really doesn't have a lot more to it than that. The combat is kind of pants. There are no boss monsters, no real interesting fights, there is no real end-game.
Terraria is the opposite. The 2-D nature makes building less fun because you can't do as much (though making a tree-house like in the latest trailer is pretty cool, as is building sky-forts that can only be reached using a bed (to set spawn) and a "return to spawn" mirror) and the exploration consists of "run left" or "run right."
But holy goddamn is the combat so much more fun. Instead of tiered swords and a bow (ala minecraft) there's a whole bunch of stuff. Armor sets with varied bonuses (including one with high defense that has a set-bonus that makes you even more protected. Another with a set-bonus of magic regen, and so on), swords, flails, bows, muskets, pistols, high-speed rifles, laser guns, magic books/flowers/wands/sceptres. And three boss fights as well as dungeons and so on.
They share some similarities, but in the end they're wholly different in focus. Minecraft is good if you like to make things and occasionally be threatened by horrible monsters.
Terraria is good if you like to take the fight to the horrible monsters with a bit of building or mining here or there to acquire resources or build new avenues of attack/defense.
So, yeah, Terraria is worth a try (and it's only 10 dollars). My only beef with it, really, is that once you've maxed your HP and mana, collected virtually every item and killed everything, there's not of a hell of a lot to do.
But, hey, I got 24 hours of mad fun out of a 10 dollar game. That's more than you get out of most 60-dollar ones.