One of the advantages of logic programming is the fact that it offers many sources of implicit parallelism, such as and-parallelism and or-parallelism. Arguably, or-parallel systems, such as Aurora and Muse, have been the most successful parallel logic programming systems so far. Or-parallel systems rely on techniques such as Environment Copying to address the problem that branches being explored in parallel may need to assign different bindings for the same shared variable. Recent research has led to two new binding representation approaches that also support independent and-parallelism: the Sparse Binding Array and the CopyOn-Write binding models. In this paper, we investigate whether these newer models are practical alternatives to copying for or-parallelism. We based our work on YapOr, an or-parallel copying system using the YAP Prolog engine, so that the three alternative systems share schedulers and the underlying engine.