兴奋 means "excited"/"stimulated" and generally in a positive way. So if you are looking forward to something, 兴奋describes that state of mind more closely.
消息传来，人人为之兴奋。As the news arrived, people got really excited.
这是一个令人兴奋的场合。This is a very exciting occasion.
我们都为这消息感到兴奋。We were all excited by the news.
麝香被用作香料和兴奋剂。Musk is used as a fragrance and a stimulant (this shows how 兴奋 is closely related to "excite," "stimulate").
On the other hand, 激动 is closer to "emotional."
他一辩论起来就十分激动。He gets very emotional when he starts arguing.
潘是个非常容易激动的人。Pan is the type of person who easily gets emotional.
我容易激动，却不爱报复。I get emotional easily, but I do not like to seek revenge.
这段旧梦重温使我很激动。This rekindled old dream made me very emotional.
Hope this helped!