The potential for GPUs and many-core CPUs to support high performance computation in the area of computational fluid dynamics (CFD) is explored quantitatively through the example of the PPM gas dynamics code with PPB multifluid volume fraction advection. This code has already been implemented on the IBM Cell processor and run at full scale on the Los Alamos Roadrunner machine. This implementation has involved a complete restructuring of the code that has been described in detail elsewhere. Here the lessons learned from that work are exploited to take advantage of today's latest generations of multi-core CPUs and many-core GPUs. The operations performed by this code are characterized in detail after being first decomposed into a series of individual code kernels to allow an implementation on GPUs. Careful implementations of this code for both CPUs and GPUs are then contrasted from a performance point of view. In addition, a single kernel that has many of the characteristics of the full application on CPUs has been built into a full, standalone, scalable parallel application. This single-kernel application shows the GPU at its best. In contrast, the full multifluid gas dynamics application brings into play computational requirements that highlight the essential differences in CPU and GPU designs today and the different programming strategies needed to achieve the best performance for applications of this type on the two devices. The single kernel application code performs extremely well on both platforms. This application is not limited by main memory bandwidth on either device; instead it is limited only by the computational capability of each. In this case, the GPU has the advantage, because it has more computational cores. The full multifluid gas dynamics code is, however, of necessity memory bandwidth limited on the GPU, while it is still computational capability limited on the CPU. We believe that these codes provide a useful context for quantifying the costs and benefits of design decisions for these powerful new computing devices. Suggestions for improvements in both devices and codes based upon this work are offered in our conclusions.