Does the usage of the word "proud" (骄傲, 自豪, or 而荣) in Chinese differ from that in English?
Not really.  If you check the meaning of 傲 and all the associate proverb, it is not rare. Indeed, the more normal translation of "proud of someone" is 引以为傲, 以某某为敖。 

And many other associated word for proud you will rarely encounter in daily life usage , e.g. 


傲骨 ， 傲气


Some is neutral


傲岸 haughty 
傲视 despise


傲 also used negatively in following case 


傲慢 arrogant