Single-cell sequencing methodologies such as scRNA-seq and scATAC-seq have become widespread and effective tools to interrogate tissue composition. Increasingly, variant callers are being applied to these methodologies to resolve the genetic heterogeneity of a sample, especially in the case of detecting the clonal architecture of a tumor. Typically, traditional bulk DNA variant callers are applied to the pooled reads of a single-cell library to detect candidate mutations. Recently, multiple studies have applied such callers on reads from individual cells, with some citing the ability to detect rare variants with higher sensitivity. Many studies apply these two approaches to the Chromium (10x Genomics) scRNA-seq and scATAC-seq methodologies. However, Chromium-based libraries may offer additional challenges to variant calling compared to existing single-cell methodologies, raising questions for the validity of variants obtained from such a workflow. To determine the merits and challenges of various variant-calling approaches on Chromium scRNA-seq and scATAC-seq libraries, we use sample libraries with matched bulk whole-genome-sequencing to evaluate the performance of callers. We review caller performance, finding that bulk callers applied on pooled reads significantly outperform individual-cell approaches. We also evaluate variants unique to scRNA-seq and scATAC-seq methodologies, finding patterns of noise but also potential capture of RNA-editing events. Finally, we review the notion that variant calling at the single-cell level can detect rare somatic variants, providing empirical results that suggest resolving such variants is infeasible in single-cell Chromium libraries.