"Mitai" and "you" means the same.
They are 90% interchangeable.
*** What is "you"
It is 様(you), a Chinese-originated word, which means "appearance"
*** What is "mitai"
It is a broken sound of "MITA-YOU-NA",
which consts of "見た(saw/looked), 様(appearance), な".
Here you can see the word "様“ is included.
**** Gererally "you" sounds more formal than "mitai".
It is because "you" is Chinese-oriented(音読み) and "Mita" in "Mitai" is Japanese own word(訓読み). The imported Chinese words are generally regarded as of formal use. It is like the relation between Latin-originated words and its own words in English.