In most cases, these words are used in totally different contexts. 'Exuberance' means energy, vitality and enthusiasm. It's usually used with reference to people, for example, you might describe an optimistic and lively young person as being full of youthful exuberance. 'Abundance' simply means 'a lot of'. For example, 'There is an abundance of wildlife in the rainforest.'

exuberance tends to deal with more quality oriented things where abundance is a more generic word for anything of a quantity which is more than needed. Generally exuberance is used to describe somethings vitality, energy, or the positiveness of their attitude. You can use them interchangeably but I would not use "exuberance" to express an excess of something negative unless you wish to illicit a sense of irony. Hope this helps :)