Data Stream mining (DSM) is claimed to be the successor of traditional data mining where it is capable of mining continuous incoming data streams in real-time with an acceptable performance. Nowadays many computer applications evolved to online and on-demand basis, fresh data are feeding in at high speeds. Not only a decision response needs to be made rapidly, the trained decision tree models would have to be updated recurrently as frequent as the latest data arrive. By the nature of traditional data mining, training datasets are assumed structured and static, and the decision tree models are either refreshed in batches or never. That is, the full dataset will be completely scanned (sometimes in multiple repetitions), induction of rules by Greedy algorithm that proceeds in manner of divide-and-conquer in the case of constructing a C4.5 decision tree. DSM on the other hand progressively builds and renews the decision tree model at a time when a new pass of data come by. In this paper, we evaluated the performance of a popular decision tree in DSM, which is known as Hoeffding Tree vis-à-vis that of C4.5. A good mix of types of datasets was used in the experiments for investigating the apparent differences between the decision trees. An open-source DSM simulator was programmed in JAVA for the experiments.