La diferencia en español : 佩服 = admirar 羨慕 = envidia

举个例子吧 佩服 ：我真佩服他的毅力 我真佩服他的能力 羡慕：我真羡慕那些有男朋友的姑娘啊 所以个人感觉 佩服 好像严肃一点，羡慕的话就是 我也想要！

我个人的理解里，他们之间最根本的差别就是：自身的渴望与向往。羡慕就是渴望与向往你所羡慕的人达到的那个境界，希望自己也能达到那个境界。但是佩服只是单纯的尊敬与崇拜，不表示自己也渴望与向往那个境界。

羡慕：看到别人比自己好，希望自己也能和别人一样好 佩服 看到别人好，从而很尊敬甚至崇拜对方

佩服 means that you have an admiration for sb. They set up great examples for you. There are sth about him/her really make you respect and give you the motivation to improve yourself. 羡慕 means that you envy others. For example, they own sth that you dont have, or they are more competent that you in some aspects. this will encourage you to make more efforts. 佩服 is more advanced than 羡慕.