Hiragana and Katakana have many things in common, they both do not have any individual meanings and they represent a sound or a particular type of noise. These two scripts have a few major differences too. Hiragana was developed by women in an ancient period and Japanese people still consider hiragana to be feminine. Katakana was developed by Buddhist monks around the same period of time as Hiragana. Hiragana is represented by round characters while Katakana is represented by angular characters. Since these two styles do not have independent meanings individual characters are not used for writings in Japanese tattoos. A number of characters can be combined to form a word though.
The third Japanese writing style is called Kanji. It is not a native Japanese script. Kanji was adapted from Chinese writing scripts and they have individual meanings. They can represent sounds and they are in the form of pictures. Kanji is the most preferred Japanese tattoo script. Kanji has two types of sounds, one is called "on yomi" which is the original Chinese sound of a character and the other one is called "kun yomi" which is the Japanese version of the same character.
Hiragana is commonly used to represent common verbs and nouns native to Japanese in their daily routine. Katakana is used to represent foreign syllables or foreign nouns. Example includes non Japanese names like Raj, Mike, Sandy, Courtney. Kanji script is used for all purposes and has a higher number of syllables to represent native words. Kanji is not commonly used for foreign words or names. Kanji is commonly used in Japanese tattoos and is the most popular one. It is highly advised to consult a professional interpreter to translate a phrase from your language to kanji to have it on your tattoo.