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We have performed benchmarks of two three-dimensional parallel Particle-In-Cell (PIC) codes that are similar but have quite different communication patterns on different computational Grids. An electrostatic code with only electrons based on the three-dimensional skeleton PIC code employs the FFT Poisson solver that uses collective communication patterns. Another is the TRISTAN (TRI-dimensional STATNford) code parallelized with MPI, an electromagnetic full particle code, which uses a field solver that only requires point-to-point neighbor communication patterns. We present the mpptest benchmarks on cluster-based computational Grids, where both the basic point-to-point communication patterns and the basic collective communication patterns used in these PIC codes are tested. The results of these benchmarks clearly allow us to quantify and understand the scalability of both communication patterns on the Grids. The present results show that the parallelized TRISTAN code (without all-to-all collective communication) is more scalable than the parallelized skeleton PIC code (with all-to-all collective communication), in cluster-based computational Grid systems where communication performances is poor. [Copyright &y& Elsevier]