Understanding how genetic variation affects distinct cellular phenotypes, such as gene expression levels, alternative splicing and DNA methylation levels, is essential for better understanding of complex diseases and traits. Furthermore, how inter-individual variation of DNA methylation is associated to gene expression is just starting to be studied. In this study, we use the GenCord cohort of 204 newborn Europeans’ lymphoblastoid cell lines, T-cells and fibroblasts derived from umbilical cords. The samples were previously genotyped for 2.5 million SNPs, mRNA-sequenced, and assayed for methylation levels in 482,421 CpG sites. We observe that methylation sites associated to expression levels are enriched in enhancers, gene bodies and CpG island shores. We show that while the correlation between DNA methylation and gene expression can be positive or negative, it is very consistent across cell-types. However, this epigenetic association to gene expression appears more tissue-specific than the genetic effects on gene expression or DNA methylation (observed in both sharing estimations based on P-values and effect size correlations between cell-types). This predominance of genetic effects can also be reflected by the observation that allele specific expression differences between individuals dominate over tissue-specific effects. Additionally, we discover genetic effects on alternative splicing and interestingly, a large amount of DNA methylation correlating to alternative splicing, both in a tissue-specific manner. The locations of the SNPs and methylation sites involved in these associations highlight the participation of promoter proximal and distant regulatory regions on alternative splicing. Overall, our results provide high-resolution analyses showing how genome sequence variation has a broad effect on cellular phenotypes across cell-types, whereas epigenetic factors provide a secondary layer of variation that is more tissue-specific. Furthermore, the details of how this tissue-specificity may vary across inter-relations of molecular traits, and where these are occurring, can yield further insights into gene regulation and cellular biology as a whole.