Fluorescent nanoparticles have transformative potential for smartphone-based point-of-need diagnostics because an optimal material can reduce the technical burden to meet assay performance requirements. Semiconductor quantum dots (QDs) are a now well-established example of such a material. Semiconducting polymer dots (Pdots) and conjugated-polymer nanoparticles (CPNs) are emerging materials that bring advantages of brightness, synthetic ease, and being metal-free versus QDs, but frequently present the trade-off of spectrally broad emission and less well-defined surface chemistry. Here, we compare these two classes of nanoparticle in the context of a "bare bones" device that uses the smartphone for all-in-one excitation and imaging of fluorescence. The greater per-particle brightness of Pdots provides orders of magnitude better imaging sensitivity versus QDs, and this advantage translates to a model lateral flow assay. Our data suggests that Pdots will support multicolor imaging on a smartphone in an optimized assay, although QDs are likely superior for this purpose. These pros and cons lead to discussion of how physicochemical differences between QDs and Pdots may influence assay performance beyond differences in optical properties. Overall, Pdots have great potential for enabling smartphone-based fluorescence assays with high sensitivity and low detection limits.