1,意思上的区别,complain of 多了to say that you have a pain or are sick的意思,比如：She had been complaining of headaches.
另外complain of的抱怨是正式的,所以可以是法律上,向官方提出的.比如：Refugees had complained of being robbed and beaten by officials.
2.用法上的区别
complain of / complain about 是接 sth或者动名词
但是complain about 可以不带,而complain of则不行.
比如：What are you complaining about?