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.
Examples:
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."
Examples:
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!