-ず and -ぬ are two alternatives to the negative form -ない / -ません. But I noticed that depending on the word, it's either -ず or -ぬ, although it seems like some words can take both suffixes. Some examples I have encountered:

#-ず
知らず (lyric in song "touch" by Younha)
わからず (lyric in song "aisuru mono" by Angela Aki)
せず (song title: "yudan sezu ni ikou")
なれず (lyric in song "mirae he" by Kiroro)

-ぬ

気づかぬ (lyric in song "arigatou" by Kokia)
届かぬ (song title: "todokanu omoi")
ならぬ (lyric in song "shunrai" by Yellow Generation)

both -ず and -ぬ

とらず / とらぬ
できず / できぬ

So are there rules for choosing between -ず and -ぬ?