I'm sure it has been said before this but...
Terraria is a game with actual goals. It has a purpose for building things beyond "look what I made." It also has a more user friendly crafting system. Meaning you don't have to read game documentation or websites to know what items make what. If you have the mats and are near the right facilities you can make it. Very simple. Also, co-op play is where the majority of the fun is. Single player is cool, but mucking about with your buddies makes the game so much more fun. It also makes it worth replaying, imo.
Minecraft is a sandbox and nothing more. It exists solely to enable the creation of cool stuff. It requires, I feel, more creativity to fully enjoy it. If you have a creative streak in you, then Minecraft is an excellent outlet for that creative energy. You can just look at youtube to see all the amazing things people can do with the game. Minecraft can also be enjoyed a bit more solo than Terraria, imo. It is quite enthralling to have a whole world of your own creations. You can also join one of the many Minecraft servers and enjoy the game's massive number of communities to build things as a group. Like Terraria, playing with your friends adds a ton of replayability and another level of fun to the game.
In short, Minecraft has a better toolset for constructing awesome things, while Terraria is more of an actual game instead of a builder's sandbox.