I would typically have an independently calculated fold-change that I use for QC and visualization. I don't currently have a paper to reference to recommend doing some benchmarks for every project, where I would recommend testing DESeq2 / edgeR / limma-voom. However, there are some papers that cite use of that strategy here in this acknowledgement.
In other words, one way that you could tell if a method may not be optimal for your dataset if you have a known perturbation, you can visually confirm the expected change with the directly calculated log2(FPKM + 0.1) value, but that gene isn't identified as differentially expressed with one of the methods. It is kind of messy, but I do briefly mention this sort of troubleshooting strategy here.
In terms of comparing rlog values from DESeq2 and the direct FPKM / fold-change values, I do have this blog post: http://cdwscience.blogspot.com/2019/02/variance-stabilization-and-pseudocounts.html