Two major techniques commonly available for modeling genomic data are the relational and object oriented approaches. This paper discusses the strengths and weaknesses of both approaches. The comparison was done using two sets of disparate genomic data, one for the E. Coli genome and one for the human genome, in order to demonstrate the generality of the modeling methods and the credibility of the comparison itself. One major strength of the object-oriented approach is its highly flexible data modeling power offering an elegant way of representing complex genomic objects. The approach's major weakness includes the lack of generic way of accessing complex objects. The strength of the relational approach is its full provision of SQL. But the approach's weakness is cumbersome modeling of complex genomic objects that is due to normalization. This paper also includes discussions on broader issues related to the two alternative approaches such as support for ad hoc queries and a federation of heterogeneous genomic databases in which both relational and object-oriented data models are used.