First off I should get this off my chest: I think A Link Between Worlds is a better game than A Link to the Past. A Link Between Worlds was created as a sequel to A Link to the Past, meant to capture the gameplay and style of the original game while adding and changing a lot of its elements. A look at history can quickly tell anyone that ALTTP (I will be abbreviating from now on) is the MOST important game in the franchise and one of the most important games of all time.

It is no question that ALTTP paved the way for every Zelda game after and influenced countless other games in the process. As I see it though, ALBW is the superior game and here is why:
1. That Beautiful Item System
One of the key changes that not only shook up the ALTTP formula but the entirety of Zelda was the new item system. A character named Ravio has taken up residence in Link's house and runs an item shop.

The twist is that he sells the items that are required to solve dungeons and defeat their bosses. Not only that but you have the option to RENT or BUY the items. Renting puts the prices a lot lower but the catch is that if you die you lose all of your rented items and must pay for them again to get them back.

Buying is more expensive but you keep the items permanently. This system expands the freedom given to the player in regards to dungeon order. For anyone who has seen Egoraptor's Zelda Sequelitis, he mentioned how in ALTTP the dark world dungeons are numbered, giving the player the impression that the dungeons have to be beaten in order when in reality the dungeons can be done in almost in any order

ALBW encourages the player to do the dungeons in any order they please and allows them to do so. Freedom is a feature, not a secret.
2. The New and Improved Map
ALTTP's map was rudimentary, showing a general layout of the world and location of dungeons. ALBW, on the other hand, has one of the best map systems of any Zelda thus far. At first, the map looks exactly the same as ALTTP, which it almost is, but one HUGE difference has been added: PINS.

Taking a page out of the DS Zeldas book, rather than marking a map by writing with the stylus, you can mark your map with 3 different colored pins. This is EXTREMELY useful, granted not as cool as writing on the map, but is perfect for keeping track of collectibles like Heart Pieces and Maimais.

I used it constantly and when I played ALTTP, I wished I had it.
The Story and Characters
ALTTP has an iconic story and characters and some cool quest lines but they all had limited dialogue and I had a hard time connecting with them. ALBWs story was very similar but with a few twists and new characters.

I found them all to be charming and memorable, and of course, they were given more time to speak and therefore, more time to develop.

While this isn't the most important aspect of a Zelda game to have, it is nice to see more effort put into it.
The Wall Painting Transformation
Every Zelda has its gimmick and in ALBW it is the ability to meld into the wall and turn into a picture.

Very random and strange, but as are is most Zelda games and this might be one the most clever ideas ever put into a 2-D Zelda. The puzzles designed around this mechanic boggle my mind with their ingenuity. You also use it to move to and from this game's version of the dark world: Lorule.

Some will argue that the Magic Mirror is more flexible as it allows you to transport yourself into the dark world from where you are as opposed to having to find a portal in ALBWs overworld, whether it be Hyrule or Lorule, to which I agree. Other than the limiting transport capabilities between worlds, the painting transformation is as fun as it is functional and helpful.
The Visuals
This might be controversial as to whether the new art style is TRULY an improvement over ALTTP, and all reasons are purely subjective but it is objective to say the graphics and details have greatly improved.

As to which style I personally prefer, I love them both for different reasons: ALTTP has iconic sprite work and the art is familiar, vibrant, and the best the SNES had to offer at the time. ALBW uses a chibi 3-D art style with everything looking polished and shiny. I would say that ALTTP has more variety, being able to adopt both bright and dark color palettes while ALBW seemed to always be bright, more kid-friendly. In that way, ALTTP is more diverse in the moods its art can invoke while ALBW has a little more trouble distinguishing itself as dark when it needs to be dark.

ALTTP I guess wins a little bit more for me, but ALBW did something right that ALTTP got hilariously wrong: the color of Link's hair.

When it comes to the promotional art for ALBW on the other hand, I vastly prefer the watercolor work than the art of ALTTP but again that is just me.

Everything else in the game is just as you would expect from any Zelda game: The dungeons and puzzles are on par if not better and more genius than ALTTP. The combat has stayed largely the same but with one MAJOR change: NO MAGIC METER.

All magic is now tied to a Stamina Meter that refills over time. Why the change? Well, now not only do spells and magic items consume the meter but so does the painting transformation and shooting arrows.

It seems strange at first but arrows are unlimited so there is no need to look for them lying around because you can fire as many as your stamina allows. Is this better? I personally think so as it was annoying when I ran out of magic in ALTTP but I do think it is odd that they didn't do the same for bombs, but I guess bombs are more powerful so maybe it was a balance issue. For music, ALBW does its own renditions of ALTTPs tracks and adds its own and both sound incredible, I mean they sound like they were performed by a live orchestra.

One last comparison between ALBW and ALTTP is that ALBW is a far easier game in my own opinion.

I died a lot in ALTTP, but that is not to say ALBW is easy, I died exploring dangerous areas unprepared.
Overall The Legend of Zelda A Link Between Worlds is a masterpiece and updated the formula established by A Link to the Past marvelously and is a must-play for any Zelda fan and owner of a 3DS.
