If I have a PCR free high coverage bam and a low coverage bam and I downsample the PCR free high coverage bam to the same coverage as the low coverage bam, would I then expect the variants called from each of the two bams to be different?
There probably will be some differences.
The low coverage BAM may have not have a sufficient number of reads to reliably call some heterozygous sites, or may call some heterozygous sites as homozygous if the few reads at such a position are mostly from the alternate allele. The low coverage BAM may also have some PCR errors.
The high coverage BAM should not encounter these issues, and downsampling should not affect this, unless you have downsampled too much. Differences in variant calls between the high coverage BAM and the downsampled high coverage BAM could indicate excessive downsampling.