I was studying the difference between these two forms, that actually I cannot quite understand. One of the differences seems to be that ために can be used with volitional forms such as たい and ろう、while ように can be used with both the volitional form and the potential. Did I understand correctly?
My understanding is that ように is used with potential or based on the condition being out of the speakers control, so using volitional is fine.
Whereas ために implies the the speaker has control to make something happen. Though to echo virmaior I have never seen たい used with them.
Similar types of answers have been posted on the difference here: Difference between ために and ように and https://www.reddit.com/r/LearnJapanese/comments/1figyo/difference_between_%E3%82%88%E3%81%86%E3%81%AB_and_%E3%81%9F%E3%82%81%E3%81%AB/