I've never played Terraria before so I can't compare this game to it; however, I can say this. Starbound is an excellent game, especially for an early access title! I bought it back in December, 2013 and the game has drastically changed since then (in a good way). The development started out a bit slow, but as of the beginning of this year, Chucklefish has really picked up their pace with delivering content. They put up blog posts about their current progress on their home page most weekdays and they even have a seperate branch of the game that you can opt into which is updated every night, although it can be quite buggy. Chucklefish is very transparent with this game and they actually reach out to the community for ideas and feedback. I've seen them pop up on the official forums several times. They've also incorporated a few community made mods into the game as well.
As for the game itself, it has a lot of the things you would expect a sandbox game to have. Procedurally generated worlds, a crafting system, lots of items, monsters, dungeons, loot, etc. There also used to be survival elements like hunger and temperature, but they were removed since the devs werent happy with its current implementation. The survival elements might make a return in the future, but there's no guarantee of it.
Starbound is about exploration and if you're jumping into it for the first time, there's a lot to see. Plenty of planetary biomes, special minibiomes, underground biomes and structures like villages and dungeons to boot. There's also a lot of cool things you can find like costumes, hats, musical instruments that can play any .abc file, randomly generated weapons and shields and even fun items like water balloons, snowball miniguns and gnomes that shoot rainbows. Exploration is even more fun if you can get a couple of friends on board with you.
This game is also very flexible in terms of customization. As of right now, there are seven different species to choose from, all with their own lore. You get to decide what you character's name is, what species they are, what gender they are, how they look and what kind of clothes they start out with. There's also different difficulties you can choose from at the character creation screen, but they aren't that much different at the moment unfortunately. Each species has their own style of space ship and they can be expanded with ship upgrades as you progress through the game. You can decorate your ship with anything you craft or find on your adventures. You can even create large scale constructions on planets if you're so inclined. There's a huge variety of building materials (way more than Minecraft), which allows you to construct some really cool things.
Another very important thing worth noting is that Starbound is incredibly mod friendly. When they say that the game was built from the ground up to support mods, they aren't kidding. Even if you have no programming experience, it's still possible for you to create very nice mods using just JSON alone. This is true because I can say that from experience.
If you're looking for a 2D space exploration sandbox game, Starbound has you covered. And since it's still in early access, it's only going to keep getting better. Chucklefish even stated that they've made enough money to support this game for another nine years and they plan to continue updating this game well after release. Starbound is definitely worth the $15 and I highly recommend you get it. The devs are nice, the community is nice and the game is great! Get it, you won't regret it (probably).