You can do more or less the same with e.g. objdump, but the root difference is that DOS COM binaries are very simple: basically a tiny header then the whole program in a big chunk.

More modern formats (be it PE, ELF, Mach-o, ...) are far more complex, with many different segments, running in a more complex CPU mode, generally dynamically linked, and all the other bell and whistles. So even if you had an identical debug.exe for Linux, it would still be much harder to make sense of.