Both mean to travel. However, the purpose of 旅游 is to have fun, like 我喜欢旅游．(i like traveling) and 旅行 is more meaningful and rewarding, it has the meaning of journey. It's the difference between entertainment and experience. This is the reason why 旅行 can be used as a metaphor for life but 旅游 can't.ex: 人生是一次旅行。( Life is a journey). In addition, some words and phrases are set, like we say 旅行社　instead of 旅游社。

旅遊 means for fun. 旅行 means for fun or for work.

God knows