I think that the exploitation was a result of the greed that came with the exploration. Countries were in a race to discover as much and claim as much as they could. The exploitation occurred as a result of this.
Are you asking which term we think is more appropriate? If so, I would argue that "Age of Exploitation" would clearly be more accurate in terms of what really happened.
It is true that there was a great deal of exploration that went on during this time. And some of the exploration, at least, was for the sake of knowledge. But that was not the main point of the exploration. It is hard to argue that the Europeans were not mainly exploring so as to be able to exploit the lands and the routes that they found. They were trying to get around Africa so as to trade with the Spice Islands. Columbus was trying to find an easier way to those same islands. Later on, once the New World was "found," exploration within it was clearly for the purpose of finding valuable things that could be sent back to Spain.
Although the phrase "Age of Exploitation" is a bit pejorative, it probably comes closer to being accurate because the Europeans were more interested in exploiting what they found than in exploring for the sake of gaining knowledge.