Utada Hikaru has always been so hit-or-miss to me. Because she is popular and writes her lyrics she receives praise, but I don't think that makes her a best lyricist. She's not terrible (although some of her English tracks made me frown), but neither is she particularly superior from what I can tell. I always felt she was more about overall sound, being particularly innovative in her composing, rather than lyrics.
I cannot really name a worst lyricist, but as far as best--
I am surprised (or maybe not) that anybody has yet to mention
KOKIA. Aside from being one of the most
incredible vocalists I have ever heard, her lyrics are like poetry. A different style from Ayu's, but deep and well-crafted nonetheless. I was speaking with a Japanese friend of mine, and he explained to me that, particularly in their native Japanese form, KOKIA is a master lyricist. The translations don't quite convey her ability to use her native language.
Some do, though. Such as
Arigatou,
Time to Say Goodbye, and
The Power of Smile. The song "Harmony (Chouwa Oto)" was partially written in code.
Daijina Mono wa Mabuta no Ura ni is one of the most heart-wrenching songs I've ever heard.