There are a handful of methods of input pinyin is taught in China and Zhuyin is taught in Taiwan.

Pinyin is romanized and much easier to learn in my opinion but mashes similar sounds together in a confusing way that isn’t obvious. Zhuyin uses a Chinese derives writing system and is more accurate towards how it’s pronounced but a little more difficult to learn especially for foreigners.

There’s a good podcast episode, maybe overheard at National Geographic on the wubi method and why the creator thinks it’s the best. Essentially pre-pinyin this genius guy came up with another method of input that even today is the fasted way to input Chinese but not as easy to learn as pinyin. Pinyin also carries over some ideological baggage as China wants everyone to learn the same first language at least so the main method of learning and input is pinyin. This is annoying for dialect speakers who have to type pinyin even when the pronunciation is off like Sichuanese or not even the same language like Cantonese.