Vico et al. (2016) suggest a fast algorithm for computing volume potentials, beneficial to fields with problems requiring the solution of the free-space Poisson's equation, such as beam and plasma physics. Currently, the standard is the algorithm of Hockney and Eastwood (1988), with second order in convergence at best. The algorithm proposed by Vico et al. converges spectrally for sufficiently smooth functions i.e. faster than any fixed order in the number of grid points. We implement a performance portable version of the traditional Hockney-Eastwood and the novel Vico-Greengard Poisson solver as part of the IPPL (Independent Parallel Particle Layer) library. For sufficiently smooth source functions, the Vico-Greengard algorithm achieves higher accuracy than the Hockney-Eastwood method with the same grid size, reducing the computational demands of high resolution simulations since one could use coarser grids to achieve them. Additionally, we propose an improvement to the Vico-Greengard method which further reduces its memory footprint. This is important for GPUs, which have limited memory, and should be taken into account when selecting numerical algorithms for performance portable codes. Finally, we showcase performance through GPU and CPU scaling studies on the Perlmutter (NERSC) supercomputer, with efficiencies staying above 50% in the strong scaling case. To showcase portability, we also run the scaling studies on the Alps supercomputer at CSCS, Switzerland and the GPU partition of the Lumi supercomputer at CSC, Finland.