As a Zelda fan that has played every title, I did not like this game at all. Breath of the Wild's formula is not faithful to the elements that made the Zelda franchise so enjoyable.
1) No item progression: All in-game items are obtained from the plateau tutorial. This is such a shame because one of the most exciting feelings from previous titles is obtaining a new item from a dungeon. (I will never forget how cool obtaining the spinner or the whip was). This means that the combat gameplay doesn't change during your playthrough, hence fighting enemies becomes dull and repetitive.
2) No interesting story or characters: One of the things that the franchise is most known for is how charming its story and characters are. BoTW's story is very lazy in my opinion. Using the amnesia and memories plot is cliche. Not to mention that none of the characters were likeable. BoTW Zelda is hands down the worst one. There was always a sense of mystery surrounding zelda's character. Not anymore. Now she's just daddy's girl trying to awaken her power *yawn*. The voice acting did not help either. Furthermore, we only saw the champions through memories (another lazy plot...) . They had a little bit of potential but I doubt they would ever come close to the character development Midna or even Linebeck had. Most importantly, no sidekicks :(
3) Lackluster plot: Previous zelda games had a very strong plot. As the story progressed, meaningful events occurred that built up the tension between the hero and the reincarnation of evil. This game only has 5-6 main quests that are filler events adding next to nothing to the plot. Even if this game is open world, it does not excuse the lack of any story. Skyrim and The Witcher 3 had a captivating story. In conclusion, you run around doing nothing meaningful until you decide to defeat Ganondorf.
4) Unrewarding exploration: There is no point in exploring Hyrule in Breath of the Wild. The world is so big yet so empty. You will ALWAYS find one of these things while exploring, namely either a) korok seed b) shrine c) the same enemies you've been encountering for the past 30 hours. There is nothing rewarding about any of these. Sure, you get an extra heart, inventory slot and upgraded gear, but then what do you do with these things? Nothing except repeating the same thing over and over again.
5) OK Dungeons: Dungeons and Zelda go hand in hand. Dungeons were always rightfully a huge part of the previous games. BoTW's dungeons' premise is to activate 5 terminals in order to be able to fight the boss (another blight ganon...). While I do appraise the new idea of being able to control certain parts of the divine beast, the puzzles were not nearly as complex and satisfying as previous titles. Where did items and keys go? Anyways, I was always excited to see what was waiting for me behind a boss's door. Not in BoTW. The dungeons have exactly the same theme and boss design. You don't have to figure out how to defeat the bosses in BoTW because 5 bomb arrows will do the trick.
6)Average Music: I find the music in zelda games to be extremely important. The songs would always capture perfectly the essence of the game in a way I can't describe. Unfortunately, the music in BoTW does not fairly capture the charm of the zelda series.
7) No Puzzle Solving: One major thing about the franchise was figuring out how to complete a certain task, whether it was obtaining a certain item or unlocking a new area, by using logic and the items at your disposal. There are no such quests in BoTW. BoTW is not centered around puzzle solving rather around defeating enemies repetitively to upgrade your gear.