给你看朗文的英文解释吧，比中文详细而且直观
luxurious:very expensive, beautiful, and comfortable
extravagant:1.spending or costing a lot of money, especially more than is necessary or more than you can afford
2.doing or using something too much or more than is necessary
3.if someone makes extravagant claims, promises etc, they make big claims or promises that are not true or real
4.very impressive because of being very expensive, beautiful etc
这样比较直观了吧，extravagant的词义更加宽泛，luxurious词义比较单一。
PS：如果自己有一定的英文基础的话，查单词最好还是直接看英文注解，配合给出的例句，能够让你更加准确的理解这个词在英语语系中的含义和用法。推荐朗文当代英语词典（第四版）