If I have two assembled genomes (one reference), what is the difference between doing SNP calling using something like Samtools from the raw Illumina reads and doing a Mauve alignment after assembly of each genome? Would Samtools be much more accurate? It seems easier to just do a Mauve alignment and extract the SNPs since I've already done the assemblies but maybe this is oversimplifying it. These are bacterial genomes if that matters.
You should use the reads and
samtools if you have them. Part of identifying SNPs etc is determining how well they're supported (i.e. are they real or sequencing errors for instance). If you aligned 2 genomes with mauve, firstly it will be horribly inaccurate as you say, but also you'll have no information about whether that SNP is supported in most or all of the reads covering that position.