两者区别：be careful with表示做某事时很小心、仔细或对某人某物很关心。with后接名词或动名词，be careful of意思是当心；留意；注意，后接名词、动名词或从句，形容人很细心。
be careful with造句：You are careful with my cat。你对我的猫很关心。We’ve got to be careful with everything we do。我们做任何事都要仔细。Be careful with that knife.It’s got a keen edge。小心那把刀子，他有锐利的锋刃。
be careful of造句：Be careful of the dog，it sometimes bites people。当心那条狗，它有时候会咬人。Be careful of that sinister man，He is dangerous。留意那个阴险的人，他很危险。You must be careful of your health。你一定要注意你的健康。