Zhuyin and Pinyin, from a logical point of view are identical. One can be transcribed into the other using a table (or computer), no linguistic experience is needed. You can reverse the process and end up with the same text as you start with. There is no abiguity as there might be translating from Chinese->English->Chinese.
As many have commented, it is just a way to represent the sounds. How well you render the text as speech depends on your skill, but a native speaker who understood the symbols would not have a problem.
The real issue with Zhuyin and Pinyin seems to be one of practicality (and politics). I know and use both since I live in Taiwan:
Pinyin is great for computers, I can touch type in English, therefore I can touch type in Chinese (as long as I know the characters!) Actually quite a few native speakers at my work use Pinyin for computer entry.
Pinyin is used in Chinese education everywhere except Taiwan, so most Chinese learning material uses Pinyin.
Pinyin can be transcribed by most foreigners, even if they cannot render it as speech. My mum can write my address legibly in roman characters, but not using Chinese ones. Foreigners can also compare words, even when they do not know the meaning, street names for example. It is harder in Zhuyin without training.
Pinyin is useful in Mainland China or on Mainland chat boards if you don’t use characters, yet want to communicate (The strong romanization system of Japanese is also used to advantage in this way by Japanese)
Zhuyin is useful for reading Taiwan children’s books, a good way to practice reading. It is also useful for reading Taiwanese educational material.
Taiwanese poeple can tell you the correct pronunciation of words to you if you know how the system works.
Zhuyin can be mixed with Chinese characters more easily than Pinyin, and with better asthetic effect.
Zhuyin can be written with a brush (should you care).
Pinyin’s great weakness is that the accent marks, critical for correct tone, are not always transcribed (Beijing street signs have this problem!)
For my opinion though, I see little value in Zhuyin. It is just another system you have to learn in a language plagued by complexity in the writing system (two sets of characters, three romanization systems, many computer input methods, Zhuyin etc.) Linguistics and writing are made easier by having fewer alphabets. Imagine for instance how much harder it would be to learn French (if you spoke Spanish) if you had to start by learning a new writing system.
Don’t forget though, neither Zhuyin nor Pinyin are commonly used as writing systems in the Chinese speaking world. They are only aids to education and pronunciation. To achive a high standard of Chinese literacy, and appreciation for Chinese culture, you must learn characters.