Therefore if you're trying to get both cores working, you need to make redundant copies of your original bios files so that your 'system/dc' folder contained all four file names: Reicast requires 'dc_boot.bin' and 'dc_flash.bin' while Redream requires just 'boot.bin' and 'flash.bin'. This detail is easy to miss in the documentation, and I believe a few early posts on the Redream core quoted its filenames incorrectly.
After rigorous testing, against Reicast and Redream crashes I've determined that each Dreamcast core requires a different pair of filenames for the bios.