The problems of Data Integration/Exchange (DE) and Ontology Based Data Access (OBDA) have been extensively studied across different communities. The underlying problem is common: using a number of differently structured data-sources mapped to a mediating schema/ontology/knowledge-graph, answer a query posed on the latter. In DE, forward-chaining algorithms, collectively known as the chase, transform source data to a new materialised instance that satisfies the ontology and can be directly queried. In OBDA, backward-chaining algorithms rewrite the query over the source schema, taking the ontology into account, in order to execute the rewriting directly on the sources. These two reasoning approaches have seen an individual rise in algorithms, practical implementations, and benchmarks. However, there has not been a principled methodology to compare solutions across both areas. In this paper we provide an original methodology and a benchmark infrastructure - a set of test scenarios, generator and translator tools, and an experimental infrastructure - to allow the translation and execution of a DE/OBDA scenario across areas and among different chase and query-rewriting systems. In the process, we also present a syntactic restriction of linear Tuple Generating Dependencies that precisely captures DL-Lite R , a correspondence previously uninvestigated. We perform cross-approach experiments under a wide range of assumptions, such as the use of different source-to-target mapping languages, shedding light to the interplay between forward-and backward-chaining. Our preliminary results show that, indeed, chase can compete and might overcome query rewriting even in the face of large data especially for complex mapping languages.