Mining with big data or big data mining has become an active research area. It is very difficult using current methodologies and data mining software tools for a single personal computer to efficiently deal with very large datasets. The parallel and cloud computing platforms are considered a better solution for big data mining. The concept of parallel computing is based on dividing a large problem into smaller ones and each of them is carried out by one single processor individually. In addition, these processes are performed concurrently in a distributed and parallel manner. There are two common methodologies used to tackle the big data problem. The first one is the distributed procedure based on the data parallelism paradigm, where a given big dataset can be manually divided into n subsets, and n algorithms are respectively executed for the corresponding n subsets. The final result can be obtained from a combination of the outputs produced by the n algorithms. The second one is the MapReduce based procedure under the cloud computing platform. This procedure is composed of the map and reduce processes, in which the former performs filtering and sorting and the later performs a summary operation in order to produce the final result. In this paper, we aim to compare the performance differences between the distributed and MapReduce methodologies over large scale datasets in terms of mining accuracy and efficiency. The experiments are based on four large scale datasets, which are used for the data classification problems. The results show that the classification performances of the MapReduce based procedure are very stable no matter how many computer nodes are used, better than the baseline single machine and distributed procedures except for the class imbalance dataset. In addition, the MapReduce procedure requires the least computational cost to process these big datasets.