We propose a new and effective statistical framework for identifying genome-wide differential changes in epigenetic marks with ChIP-seq data or gene expression with mRNA-seq data, and we develop a new software tool EpiCenter that can efficiently perform data analysis. The key features of our framework are: (i) providing multiple normalization methods to achieve appropriate normalization under different scenarios, (ii) using a sequence of three statistical tests to eliminate background regions and to account for different sources of variation and (iii) allowing adjustment for multiple testing to control false discovery rate (FDR) or family-wise type I error. Our software EpiCenter can perform multiple analytic tasks including: (i) identifying genome-wide epigenetic changes or differentially expressed genes, (ii) finding transcription factor binding sites and (iii) converting multiple-sample sequencing data into a single read-count data matrix. By simulation, we show that our framework achieves a low FDR consistently over a broad range of read coverage and biological variation. Through two real examples, we demonstrate the effectiveness of our framework and the usages of our tool. In particular, we show that our novel and robust 'parsimony' normalization method is superior to the widely-used 'tagRatio' method. Our software EpiCenter is freely available to the public.